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530 relations: A4 polytope, Abel–Ruffini theorem, Absolute convergence, Abstract algebra, Advantage (cryptography), Alternating group, Alternating permutation, Alternating polynomial, Alternative algebra, Analysis of similarities, Ancestral reconstruction, Andrew M. Gleason, Anti-diagonal matrix, Anti-proverb, Anticommutativity, Antisymmetrizer, Anton Kotzig, Arbitrariness, Ars Conjectandi, Asymmetric graph, Automorphism, Average, Évariste Galois, Barycentric subdivision, BassOmatic, Baxter permutation, Bayesian hierarchical modeling, Bell number, Big data, Bijection, Bijection, injection and surjection, Bikini Beach, Binary heap, Binary octahedral group, Bingo (U.S.), Binomial coefficient, Birthday problem, Bit-reversal permutation, Bitruncated cubic honeycomb, Block cipher, Blossom (functional), Board (bridge), Bogosort, Bond fluctuation model, Book embedding, Boolean algebras canonically defined, Boundedly generated group, Braid group, Burr puzzle, Burrows–Wheeler transform, ..., Cable knitting, Campanology, Candidate key, Cantellated 5-cell, Cantellated 5-cubes, Cantellated 5-orthoplexes, Cantellated 6-orthoplexes, Cantellated 7-simplexes, Cantellated 8-simplexes, Carrick bend, Cartesian tree, Catalan number, Cayley's mousetrap, Cayley's theorem, Change ringing, Chebotarev's density theorem, Chinaman, Laundryman, Chord names and symbols (popular music), Chordioid, CIKS-1, Ciphertext, Circle of fifths, Circular layout, Circular shift, Clifford algebra, Closure with a twist, Coefficient of fractional parentage, Coffman–Graham algorithm, Combination, Combination lock, Combinatorial proof, Combinatorial species, Combinatorics, Competitive Lotka–Volterra equations, Composition series, Compound of three cubes, Compound of two snub cubes, Computing the permanent, Configuration entropy, Conjugacy class, Contract bridge probabilities, Cooley–Tukey FFT algorithm, Cooperative game theory, Cost price, Costas array, Counting, Covering space, Cross-ratio, Cryptanalysis, Currant Events, Cycle decomposition, Cycle decomposition (graph theory), Cycle index, Cycle sort, Cycles and fixed points, Cyclic (mathematics), Cyclic order, Cyclic permutation, Damm algorithm, Daniel Kráľ, Data Encryption Standard, De Bruijn sequence, De Bruijn's theorem, Definitions of fascism, Derangement, Desargues configuration, Dessin d'enfant, Determinant, Detrended correspondence analysis, Dickson polynomial, Differentiation in Fréchet spaces, Digit-reassembly number, Digital signature, Dihedral group of order 6, Discrete mathematics, Disposition (disambiguation), Double factorial, DRYAD, Duality (projective geometry), Dyadic rational, E. Morton Jellinek, E8 (mathematics), E8 lattice, Editor war, Eight queens puzzle, Electroacoustic music, Emmy Noether, Empty set, Endomorphism, Enigma machine, Enumeration, Enumerative combinatorics, Equivalence relation, Equivalent definitions of mathematical structures, Erich Buchholz, Eulerian number, Event symmetry, Exact differential, Exchangeable random variables, Exterior algebra, External (mathematics), External memory algorithm, Factorial, Factorial moment measure, Factorial number system, Falling and rising factorials, Fano plane, Farthest-first traversal, Feedback arc set, Fialka, Filtration (mathematics), Finite group, Fisher–Yates shuffle, Football pools, Function composition, Functional principal component analysis, Galois theory, Gambler's fallacy, Gambling mathematics, Gaussian integral, Gear Cube, Generative art, Generative design, Generic programming, Genocchi number, Ghost Leg, Gilbert–Shannon–Reeds model, Gilbreath shuffle, GNU Scientific Library, Golomb–Dickman constant, Grace–Walsh–Szegő theorem, Graded poset, Grandi's series, Grandsire, Graph automorphism, Graph canonization, Graph coloring, Gray code, Grönwall's inequality, Grill (cryptology), Group (mathematics), Group action, Group representation, Group theory, H4 polytope, Haecceitism, Hall's universal group, Haploview, Heap (mathematics), Heap's algorithm, Heinrich August Rothe, Held–Karp algorithm, Heptellated 8-simplexes, Hewitt–Savage zero–one law, Higher-dimensional gamma matrices, History of group theory, History of mathematical notation, Hoffman–Singleton graph, Holomorph (mathematics), Homography, HP 35s, Hypercube graph, Hypergraph, Identical particles, In-place matrix transposition, Inclusion–exclusion principle, Income inequality metrics, Incomplete gamma function, Independent and identically distributed random variables, Index of combinatorics articles, Indicator value, Infinite conjugacy class property, Information oriented software development, Integer lattice, Integral transform, Interval exchange transformation, Invariant theory, Inversion (discrete mathematics), Inversion (music), Involution (mathematics), Joe Beevers, Jorge Luis Borges and mathematics, Journal of Modern Applied Statistical Methods, Jumble algorithm, Kakuro, Karma in Jainism, Katalin Vesztergombi, Kolakoski sequence, Kolmogorov extension theorem, Kreuzspiel, Lady tasting tea, Lai–Massey scheme, Landau's function, Langford pairing, Laplace expansion, Large numbers, Latin square, Layered graph drawing, Learning to rank, Lebedev quadrature, Lehmer code, Leibniz formula for determinants, Levi-Civita symbol, List of cycles, List of factorial and binomial topics, List of Greek and Latin roots in English/M, List of group theory topics, List of Latin words with English derivatives, List of logarithmic identities, List of matrices, List of patent claim types, List of permutation topics, List of regular polytopes and compounds, List of small groups, List of terms relating to algorithms and data structures, Longest increasing subsequence, Loopless algorithm, Lubell–Yamamoto–Meshalkin inequality, Lyndon word, Magic hypercube, Major index, Majorization, Manin matrix, Marian Rejewski, Mathematical beauty, Mathematical object, Mathematics education, Mathematics, Form and Function, Matrix (music), Max Frisch, Maxwell–Boltzmann statistics, Möbius–Kantor configuration, Meander (mathematics), Mental poker, Method ringing, Microarray analysis techniques, Microsoft Analysis Services, Miklós Bóna, Mixed radix, Modern Arabic mathematical notation, Muirhead's inequality, Multi-party fair exchange protocol, Multilinear form, Multinomial theorem, Muneer Ahmad Rashid, Natural computing, Necklace (combinatorics), New Data Seal, No free lunch in search and optimization, Nomos Alpha, Non-negative matrix factorization, NPR (disambiguation), Nuclear fuel cycle, Object–verb–subject, Oblivious ram, Optimization problem, Order, Order (mathematics), Orientation (vector space), Oriented matroid, Orthogonal array, Orthogonal array testing, Outline of arithmetic, Outline of discrete mathematics, Palindrome, Pancake sorting, Paracompact uniform honeycombs, Parastatistics, Parimutuel betting, Parity of a permutation, Parry–Daniels map, Partial permutation, Path-ordering, P′′, Pólya enumeration theorem, Pearson hashing, Perm (disambiguation), Permanent (mathematics), Permutable prime, Permutation, Permutation (disambiguation), Permutation (music), Permutation automaton, Permutation box, Permutation class, Permutation graph, Permutation group, Permutation matrix, Permutation model, Permutation pattern, Permutation polynomial, Permutation representation, Permuted congruential generator, Permutohedron, Pfaffian, Place-permutation action, Placebo-controlled study, Plancherel measure, Pocket Cube, Point-to-point transit, Poker probability, Portable, Extensible Toolkit for Scientific Computation, PQ tree, PRC200, Preorder, Price index, Primeval number, Professor's Cube, Programming by permutation, Pseudorandom generator theorem, Pseudorandom permutation, Punkte, Q-analog, Q-Pochhammer symbol, Quantum field theory, Quasi-set theory, Queue number, Rabin cryptosystem, Random permutation, Rank correlation, Rank product, RC4, Real coordinate space, Rearrangement inequality, Rebound attack, Rectified 9-simplexes, Recursive tree, Relation algebra, Relational quantum mechanics, Rencontres numbers, Representation theory, Repunit, Residue-class-wise affine group, Reversible cellular automaton, Ricci calculus, Riemann series theorem, Riffle shuffle permutation, Robinson–Schensted correspondence, Robinson–Schensted–Knuth correspondence, Robson Rotation, Rook polynomial, Root system, Rotation matrix, Round-robin DNS, Rounding, Row- and column-major order, Rubik's Cube, Rubik's Cube group, Runcinated 5-cell, Runcinated 5-orthoplexes, Runcinated 5-simplexes, Runcinated 6-cubes, Runcinated 6-orthoplexes, Samuel Beckett, Second quantization, Second-order cellular automaton, Separable permutation, Separable polynomial, Septic equation, Sequent, Sesquilinear form, Set notation, Shape, Shapley value, Shen Kuo, Shift matrix, Significance analysis of microarrays, Simple group, Simulated annealing, Skew and direct sums of permutations, Skew-merged permutation, Sort (C++), Sorting algorithm, Spectr-H64, Speedcubing, Spekkens toy model, SPQR tree, Stack-sortable permutation, Stanley symmetric function, Steinhaus–Johnson–Trotter algorithm, Stericated 5-cubes, Stirling number, Stirling numbers and exponential generating functions in symbolic combinatorics, Stirling numbers of the first kind, Stirling permutation, Straight-five engine, Substitution–permutation network, Summation, Superpattern, Sylvie Corteel, Symmetric Boolean function, Symmetric function, Symmetric game, Symmetric group, Symmetric inverse semigroup, Symmetric polynomial, Symmetric product (topology), Symmetric tensor, Symmetry in mathematics, Symmetry operation, Symplectic matrix, SymPy, Szymanski's conjecture, Talpiot Tomb, Telephone number (mathematics), Tensor product, Tessellation, Tetrahedral symmetry, The Art of Computer Programming, The Computer Language Benchmarks Game, The Engine, The Library of Babel, The Number Devil, The Prisoner of Benda, The Schoolmaster's Assistant, Being a Compendium of Arithmetic both Practical and Theoretical, Three-letter acronym, Timeline of algebra, Timeline of geometry, Timeline of mathematics, Timeline of numerals and arithmetic, Tompkins–Paige algorithm, Tracy–Widom distribution, Translation surface, Transpose, Transposition cipher, Travelling salesman problem, Truncated 5-orthoplexes, Truncated 6-orthoplexes, Truncated 7-cubes, Truncated 7-orthoplexes, Truncated 8-cubes, Truncated 8-orthoplexes, Truncated cuboctahedron, Truncated dodecadodecahedron, Truncated octahedron, Truth value, Turbo code, Twelvefold way, Unconditional convergence, Unified neutral theory of biodiversity, Uniform 6-polytope, Uniform honeycombs in hyperbolic space, Uniform matroid, Unique games conjecture, Uniquely colorable graph, Universal point set, Up to, V-Cube 6, V-Cube 8, Variably Modified Permutation Composition, Vendor lock-in, Verbal arithmetic, Verhoeff algorithm, Vexillary permutation, Virial coefficient, Vogel plane, Volumetric display, Von Neumann–Bernays–Gödel set theory, Walsh matrix, Westminster Quarters, Wilf equivalence, William A. Veech, Writing system, X Window System core protocol, Xenocrates, Yanagisawa Wind Instruments, Yoneda lemma, Zolotarev's lemma, 100 prisoners problem, 120-cell, 163 (number), 223 (number), 225 (number), 226 (number), 24-cell, 3, 3D4, 4 21 polytope, 4D vector, 5040 (number). Expand index (480 more) »
A4 polytope
In 4-dimensional geometry, there are 9 uniform polytopes with A4 symmetry.
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Abel–Ruffini theorem
In algebra, the Abel–Ruffini theorem (also known as Abel's impossibility theorem) states that there is no algebraic solution—that is, solution in radicals—to the general polynomial equations of degree five or higher with arbitrary coefficients.
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Absolute convergence
In mathematics, an infinite series of numbers is said to converge absolutely (or to be absolutely convergent) if the sum of the absolute values of the summands is finite.
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Abstract algebra
In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures.
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Advantage (cryptography)
In cryptography, an adversary's advantage is a measure of how successfully it can attack a cryptographic algorithm, by distinguishing it from an idealized version of that type of algorithm.
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Alternating group
In mathematics, an alternating group is the group of even permutations of a finite set.
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Alternating permutation
In combinatorial mathematics, an alternating permutation (or zigzag permutation) of the set is an arrangement of those numbers so that each entry is alternately greater or less than the preceding entry.
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Alternating polynomial
In algebra, an alternating polynomial is a polynomial f(x_1,\dots,x_n) such that if one switches any two of the variables, the polynomial changes sign: Equivalently, if one permutes the variables, the polynomial changes in value by the sign of the permutation: More generally, a polynomial f(x_1,\dots,x_n,y_1,\dots,y_t) is said to be alternating in x_1,\dots,x_n if it changes sign if one switches any two of the x_i, leaving the y_j fixed.
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Alternative algebra
In abstract algebra, an alternative algebra is an algebra in which multiplication need not be associative, only alternative.
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Analysis of similarities
Analysis of similarities (ANOSIM) is a non-parametric statistical test widely used in the field of ecology.
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Ancestral reconstruction
Ancestral reconstruction (also known as Character Mapping or Character Optimization) is the extrapolation back in time from measured characteristics of individuals (or populations) to their common ancestors.
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Andrew M. Gleason
Andrew Mattei Gleason (19212008) was an American mathematician who as a young World War II naval officer broke German and Japanese military codes, then over the succeeding sixty years made fundamental contributions to widely varied areas of mathematics, including the solution of Hilbert's fifth problem, and was a leader in reform and innovation in teaching at all levels.
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Anti-diagonal matrix
In mathematics, an anti-diagonal matrix is a matrix where all the entries are zero except those on the diagonal going from the lower left corner to the upper right corner (↗), known as the anti-diagonal.
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Anti-proverb
An anti-proverb or a perverb is the transformation of a standard proverb for humorous effect.
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Anticommutativity
In mathematics, anticommutativity is a specific property of some non-commutative operations.
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Antisymmetrizer
In quantum mechanics, an antisymmetrizer \mathcal (also known as antisymmetrizing operator) is a linear operator that makes a wave function of N identical fermions antisymmetric under the exchange of the coordinates of any pair of fermions.
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Anton Kotzig
Anton Kotzig (22 October 1919 – 20 April 1991) was a Slovak–Canadian mathematician, expert in statistics, combinatorics and graph theory.
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Arbitrariness
Arbitrariness is the quality of being "determined by chance, whim, or impulse, and not by necessity, reason, or principle".
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Ars Conjectandi
Ars Conjectandi (Latin for "The Art of Conjecturing") is a book on combinatorics and mathematical probability written by Jacob Bernoulli and published in 1713, eight years after his death, by his nephew, Niklaus Bernoulli.
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Asymmetric graph
In graph theory, a branch of mathematics, an undirected graph is called an asymmetric graph if it has no nontrivial symmetries.
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Automorphism
In mathematics, an automorphism is an isomorphism from a mathematical object to itself.
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Average
In colloquial language, an average is a middle or typical number of a list of numbers.
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Évariste Galois
Évariste Galois (25 October 1811 – 31 May 1832) was a French mathematician.
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Barycentric subdivision
In geometry, the barycentric subdivision is a standard way of dividing an arbitrary convex polygon into triangles, a convex polyhedron into tetrahedra, or, in general, a convex polytope into simplices with the same dimension, by connecting the barycenters of their faces in a specific way.
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BassOmatic
In cryptography, BassOmatic was the symmetric-key cipher designed by Phil Zimmermann as part of his email encryption software PGP (in the first release, version 1.0).
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Baxter permutation
In combinatorial mathematics, a Baxter permutation is a permutation \sigma \in S_n which satisfies the following generalized pattern avoidance property.
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Bayesian hierarchical modeling
Bayesian hierarchical modelling is a statistical model written in multiple levels (hierarchical form) that estimates the parameters of the posterior distribution using the Bayesian method.
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Bell number
In combinatorial mathematics, the Bell numbers count the possible partitions of a set.
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Big data
Big data is data sets that are so big and complex that traditional data-processing application software are inadequate to deal with them.
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Bijection
In mathematics, a bijection, bijective function, or one-to-one correspondence is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set.
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Bijection, injection and surjection
In mathematics, injections, surjections and bijections are classes of functions distinguished by the manner in which arguments (input expressions from the domain) and images (output expressions from the codomain) are related or mapped to each other.
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Bikini Beach
Bikini Beach is a 1964 American teen film directed by William Asher and starring Frankie Avalon and Annette Funicello.
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Binary heap
A binary heap is a heap data structure that takes the form of a binary tree.
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Binary octahedral group
In mathematics, the binary octahedral group, name as 2O or is a certain nonabelian group of order 48.
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Bingo (U.S.)
In the United States, Bingo is a game of chance in which each player matches numbers printed in different arrangements on 5×5 cards with the numbers the game host (caller) draws at random, marking the selected numbers with tiles.
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Binomial coefficient
In mathematics, any of the positive integers that occurs as a coefficient in the binomial theorem is a binomial coefficient.
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Birthday problem
In probability theory, the birthday problem or birthday paradox concerns the probability that, in a set of randomly chosen people, some pair of them will have the same birthday.
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Bit-reversal permutation
In applied mathematics, a bit-reversal permutation is a permutation of a sequence of n items, where n.
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Bitruncated cubic honeycomb
The bitruncated cubic honeycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space made up of truncated octahedra (or, equivalently, bitruncated cubes).
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Block cipher
In cryptography, a block cipher is a deterministic algorithm operating on fixed-length groups of bits, called a block, with an unvarying transformation that is specified by a symmetric key.
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Blossom (functional)
In numerical analysis, a blossom is a functional that can be applied to any polynomial, but is mostly used for Bézier and spline curves and surfaces.
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Board (bridge)
In duplicate bridge, a board is an item of equipment that holds one deal, or one deck of 52 cards distributed in four hands of 13 cards each.
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Bogosort
In computer science, bogosort (also permutation sort, stupid sort, slowsort,. shotgun sort or monkey sort) is a highly ineffective sorting function based on the generate and test paradigm.
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Bond fluctuation model
The BFM (bond fluctuation model or bond fluctuation method) is a lattice model for simulating the conformation and dynamics of polymer systems.
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Book embedding
In graph theory, a book embedding is a generalization of planar embedding of a graph to embeddings into a book, a collection of half-planes all having the same line as their boundary.
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Boolean algebras canonically defined
Boolean algebra is a mathematically rich branch of abstract algebra.
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Boundedly generated group
In mathematics, a group is called boundedly generated if it can be expressed as a finite product of cyclic subgroups.
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Braid group
In mathematics, the braid group on strands (denoted), also known as the Artin braid group, is the group whose elements are equivalence classes of n-braids (e.g. under ambient isotopy), and whose group operation is composition of braids (see). Example applications of braid groups include knot theory, where any knot may be represented as the closure of certain braids (a result known as Alexander's theorem); in mathematical physics where Artin's canonical presentation of the braid group corresponds to the Yang–Baxter equation (see); and in monodromy invariants of algebraic geometry.
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Burr puzzle
A burr puzzle is an interlocking puzzle consisting of notched sticks, combined to make one three-dimensional, usually symmetrical unit.
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Burrows–Wheeler transform
The Burrows–Wheeler transform (BWT, also called block-sorting compression) rearranges a character string into runs of similar characters.
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Cable knitting
Cable knitting is a style of knitting in which textures of crossing layers are achieved by permuting stitches.
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Campanology
Campanology (from Late Latin campana, "bell"; and Greek -λογία, -logia) is the study of bells.
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Candidate key
In the relational model of databases, a candidate key of a relation is a minimal superkey for that relation; that is, a set of attributes such that.
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Cantellated 5-cell
In four-dimensional geometry, a cantellated 5-cell is a convex uniform 4-polytope, being a cantellation (a 2nd order truncation, up to edge-planing) of the regular 5-cell.
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Cantellated 5-cubes
In six-dimensional geometry, a cantellated 5-cube is a convex uniform 5-polytope, being a cantellation of the regular 5-cube.
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Cantellated 5-orthoplexes
In five-dimensional geometry, a cantellated 5-orthoplex is a convex uniform 5-polytope, being a cantellation of the regular 5-orthoplex.
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Cantellated 6-orthoplexes
In six-dimensional geometry, a cantellated 6-orthoplex is a convex uniform 6-polytope, being a cantellation of the regular 6-orthoplex.
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Cantellated 7-simplexes
In seven-dimensional geometry, a cantellated 7-simplex is a convex uniform 7-polytope, being a cantellation of the regular 7-simplex.
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Cantellated 8-simplexes
In eight-dimensional geometry, a cantellated 8-simplex is a convex uniform 8-polytope, being a cantellation of the regular 8-simplex.
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Carrick bend
The carrick bend is a knot used for joining two lines.
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Cartesian tree
In computer science, a Cartesian tree is a binary tree derived from a sequence of numbers; it can be uniquely defined from the properties that it is heap-ordered and that a symmetric (in-order) traversal of the tree returns the original sequence.
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Catalan number
In combinatorial mathematics, the Catalan numbers form a sequence of natural numbers that occur in various counting problems, often involving recursively-defined objects.
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Cayley's mousetrap
Mousetrap is the name of a game introduced by the English mathematician Arthur Cayley.
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Cayley's theorem
In group theory, Cayley's theorem, named in honour of Arthur Cayley, states that every group G is isomorphic to a subgroup of the symmetric group acting on G. This can be understood as an example of the group action of G on the elements of G. A permutation of a set G is any bijective function taking G onto G; and the set of all such functions forms a group under function composition, called the symmetric group on G, and written as Sym(G).
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Change ringing
Change ringing is the art of ringing a set of tuned bells in a controlled manner to produce variations in their striking sequences.
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Chebotarev's density theorem
Chebotarev's density theorem in algebraic number theory describes statistically the splitting of primes in a given Galois extension K of the field \mathbb of rational numbers.
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Chinaman, Laundryman
"Chinaman, Laundryman" is a song composed by Ruth Crawford Seeger.
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Chord names and symbols (popular music)
Musicians use various kinds of chord names and symbols in different contexts, to represent musical chords.
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Chordioid
A chordioid, also called chord fragment or fragmentary voicingRawlins, Robert, et al.
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CIKS-1
In cryptography, CIKS-1 is a block cipher designed in 2002 by A.A. Moldovyan and N.A. Moldovyan.
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Ciphertext
In cryptography, ciphertext or cyphertext is the result of encryption performed on plaintext using an algorithm, called a cipher.
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Circle of fifths
In music theory, the circle of fifths (or circle of fourths) is the relationship among the 12 tones of the chromatic scale, their corresponding key signatures, and the associated major and minor keys.
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Circular layout
In graph drawing, a circular layout is a style of drawing that places the vertices of a graph on a circle, often evenly spaced so that they form the vertices of a regular polygon.
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Circular shift
In combinatorial mathematics, a circular shift is the operation of rearranging the entries in a tuple, either by moving the final entry to the first position, while shifting all other entries to the next position, or by performing the inverse operation.
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Clifford algebra
In mathematics, a Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra.
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Closure with a twist
Closure with a twist is a property of subsets of an algebraic structure.
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Coefficient of fractional parentage
In physics, coefficients of fractional parentage (cfp's) can be used to obtain anti-symmetric many-body states for like particles.
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Coffman–Graham algorithm
In job shop scheduling and graph drawing, the Coffman–Graham algorithm is an algorithm, named after Edward G. Coffman, Jr. and Ronald Graham, for arranging the elements of a partially ordered set into a sequence of levels.
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Combination
In mathematics, a combination is a selection of items from a collection, such that (unlike permutations) the order of selection does not matter.
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Combination lock
A combination lock is a type of locking device in which a sequence of symbols, usually numbers, is used to open the lock.
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Combinatorial proof
In mathematics, the term combinatorial proof is often used to mean either of two types of mathematical proof.
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Combinatorial species
In combinatorial mathematics, the theory of combinatorial species is an abstract, systematic method for analysing discrete structures in terms of generating functions.
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Combinatorics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures.
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Competitive Lotka–Volterra equations
The competitive Lotka–Volterra equations are a simple model of the population dynamics of species competing for some common resource.
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Composition series
In abstract algebra, a composition series provides a way to break up an algebraic structure, such as a group or a module, into simple pieces.
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Compound of three cubes
This uniform polyhedron compound is a symmetric arrangement of 3 cubes, considered as square prisms.
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Compound of two snub cubes
This uniform polyhedron compound is a composition of the 2 enantiomers of the snub cube.
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Computing the permanent
In linear algebra, the computation of the permanent of a matrix is a problem that is thought to be more difficult than the computation of the determinant of a matrix despite the apparent similarity of the definitions.
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Configuration entropy
In statistical mechanics, configuration entropy is the portion of a system's entropy that is related to the position of its constituent particles rather than to their velocity or momentum.
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Conjugacy class
In mathematics, especially group theory, the elements of any group may be partitioned into conjugacy classes; members of the same conjugacy class share many properties, and study of conjugacy classes of non-abelian groups reveals many important features of their structure.
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Contract bridge probabilities
In the game of bridge mathematical probabilities play a significant role.
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Cooley–Tukey FFT algorithm
The Cooley–Tukey algorithm, named after J. W. Cooley and John Tukey, is the most common fast Fourier transform (FFT) algorithm.
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Cooperative game theory
In game theory, a cooperative game (or coalitional game) is a game with competition between groups of players ("coalitions") due to the possibility of external enforcement of cooperative behavior (e.g. through contract law).
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Cost price
In retail systems, the cost price represents the specific value that represents unit price purchased.
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Costas array
In mathematics, a Costas array can be regarded geometrically as a set of n points lying on the squares of a n×n checkerboard, such that each row or column contains only one point, and that all of the n(n − 1)/2 displacement vectors between each pair of dots are distinct.
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Counting
Counting is the action of finding the number of elements of a finite set of objects.
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Covering space
In mathematics, more specifically algebraic topology, a covering map (also covering projection) is a continuous function p from a topological space, C, to a topological space, X, such that each point in X has an open neighbourhood evenly covered by p (as shown in the image); the precise definition is given below.
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Cross-ratio
In geometry, the cross-ratio, also called the double ratio and anharmonic ratio, is a number associated with a list of four collinear points, particularly points on a projective line.
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Cryptanalysis
Cryptanalysis (from the Greek kryptós, "hidden", and analýein, "to loosen" or "to untie") is the study of analyzing information systems in order to study the hidden aspects of the systems.
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Currant Events
Currant Events is the twenty-eighth book of the Xanth series by Piers Anthony, and the first book in the second Xanth trilogy.
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Cycle decomposition
In mathematics, the term cycle decomposition can mean.
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Cycle decomposition (graph theory)
In graph theory, a cycle decomposition is a decomposition (a partitioning of a graph's edges) into cycles.
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Cycle index
In combinatorial mathematics a cycle index is a polynomial in several variables which is structured in such a way that information about how a group of permutations acts on a set can be simply read off from the coefficients and exponents.
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Cycle sort
Cycle sort is an in-place, unstable sorting algorithm, a comparison sort that is theoretically optimal in terms of the total number of writes to the original array, unlike any other in-place sorting algorithm.
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Cycles and fixed points
In mathematics, the cycles of a permutation π of a finite set S correspond bijectively to the orbits of the subgroup generated by π acting on S. These orbits are subsets of S that can be written as, such that The corresponding cycle of π is written as (c1 c2... cn); this expression is not unique since c1 can be chosen to be any element of the orbit.
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Cyclic (mathematics)
There are many terms in mathematics that begin with cyclic.
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Cyclic order
In mathematics, a cyclic order is a way to arrange a set of objects in a circle.
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Cyclic permutation
In mathematics, and in particular in group theory, a cyclic permutation (or cycle) is a permutation of the elements of some set X which maps the elements of some subset S of X to each other in a cyclic fashion, while fixing (that is, mapping to themselves) all other elements of X. If S has k elements, the cycle is called a k-cycle.
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Damm algorithm
In error detection, the Damm algorithm is a check digit algorithm that detects all single-digit errors and all adjacent transposition errors.
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Daniel Kráľ
Daniel Kráľ (born June 30, 1978) is a Czech mathematician and computer scientist who works as a professor of mathematics and computer science at the University of Warwick.
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Data Encryption Standard
The Data Encryption Standard (DES) is a symmetric-key algorithm for the encryption of electronic data.
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De Bruijn sequence
In combinatorial mathematics, a de Bruijn sequence of order n on a size-k alphabet A is a cyclic sequence in which every possible length-n string on A occurs exactly once as a substring (i.e., as a contiguous subsequence).
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De Bruijn's theorem
In a 1969 paper, Dutch mathematician Nicolaas Govert de Bruijn proved several results about packing congruent rectangular bricks (of any dimension) into larger rectangular boxes, in such a way that no space is left over.
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Definitions of fascism
What constitutes a definition of fascism and fascist governments has been a complicated and highly disputed subject concerning the exact nature of fascism and its core tenets debated amongst historians, political scientists, and other scholars since Benito Mussolini first used the term in 1915.
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Derangement
In combinatorial mathematics, a derangement is a permutation of the elements of a set, such that no element appears in its original position.
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Desargues configuration
In geometry, the Desargues configuration is a configuration of ten points and ten lines, with three points per line and three lines per point.
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Dessin d'enfant
In mathematics, a dessin d'enfant is a type of graph embedding used to study Riemann surfaces and to provide combinatorial invariants for the action of the absolute Galois group of the rational numbers.
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Determinant
In linear algebra, the determinant is a value that can be computed from the elements of a square matrix.
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Detrended correspondence analysis
Detrended correspondence analysis (DCA) is a multivariate statistical technique widely used by ecologists to find the main factors or gradients in large, species-rich but usually sparse data matrices that typify ecological community data.
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Dickson polynomial
In mathematics, the Dickson polynomials, denoted, form a polynomial sequence introduced by.
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Differentiation in Fréchet spaces
In mathematics, in particular in functional analysis and nonlinear analysis, it is possible to define the derivative of a function between two Fréchet spaces.
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Digit-reassembly number
Digit-reassembly numbers, or Osiris numbers, are numbers that are equal to the sum of permutations of sub-samples of their own digits (compare the dismemberment and reconstruction of the god Osiris in Egyptian mythology).
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Digital signature
A digital signature is a mathematical scheme for presenting the authenticity of digital messages or documents.
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Dihedral group of order 6
In mathematics, the smallest non-abelian group has 6 elements.
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Discrete mathematics
Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous.
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Disposition (disambiguation)
A disposition is a tendency to act in a specified way.
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Double factorial
In mathematics, the double factorial or semifactorial of a number (denoted by) is the product of all the integers from 1 up to that have the same parity (odd or even) as.
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DRYAD
The DRYAD Numeral Cipher/Authentication System (KTC 1400 D) is a simple, paper cryptographic system employed by the U.S. military for authentication and for encryption of short, numerical messages.
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Duality (projective geometry)
In geometry, a striking feature of projective planes is the symmetry of the roles played by points and lines in the definitions and theorems, and (plane) duality is the formalization of this concept.
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Dyadic rational
In mathematics, a dyadic fraction or dyadic rational is a rational number whose denominator, when the ratio is in minimal (coprime) terms, is a power of two, i.e., a number of the form \frac where a is an integer and b is a natural number; for example, 1/2 or 3/8, but not 1/3.
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E. Morton Jellinek
Elvin Morton "Bunky" Jellinek (15 August 1890 – 22 October 1963), E. Morton Jellinek, or most often, E. M. Jellinek, was a biostatistician, physiologist, and an alcoholism researcher, fluent in nine languages and able to communicate in four others.
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E8 (mathematics)
In mathematics, E8 is any of several closely related exceptional simple Lie groups, linear algebraic groups or Lie algebras of dimension 248; the same notation is used for the corresponding root lattice, which has rank 8.
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E8 lattice
In mathematics, the E8 lattice is a special lattice in R8.
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Editor war
Editor war is the common name for the rivalry between users of the Emacs and vi (usually Vim) text editors.
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Eight queens puzzle
The eight queens puzzle is the problem of placing eight chess queens on an 8×8 chessboard so that no two queens threaten each other.
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Electroacoustic music
Electroacoustic music originated in Western art music around the middle of the 20th century, following the incorporation of electric sound production into compositional practice.
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Emmy Noether
Amalie Emmy NoetherEmmy is the Rufname, the second of two official given names, intended for daily use.
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Empty set
In mathematics, and more specifically set theory, the empty set or null set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero.
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Endomorphism
In mathematics, an endomorphism is a morphism (or homomorphism) from a mathematical object to itself.
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Enigma machine
The Enigma machines were a series of electro-mechanical rotor cipher machines developed and used in the early- to mid-20th century to protect commercial, diplomatic and military communication.
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Enumeration
An enumeration is a complete, ordered listing of all the items in a collection.
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Enumerative combinatorics
Enumerative combinatorics is an area of combinatorics that deals with the number of ways that certain patterns can be formed.
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Equivalence relation
In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive.
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Equivalent definitions of mathematical structures
In mathematics, equivalent definitions are used in two somewhat different ways.
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Erich Buchholz
Erich Buchholz (1891–1972) was a German artist in painting and printmaking.
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Eulerian number
In combinatorics, the Eulerian number A(n, m), is the number of permutations of the numbers 1 to n in which exactly m elements are greater than the previous element (permutations with m "ascents").
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Event symmetry
In physics, event symmetry includes invariance principles that have been used in some discrete approaches to quantum gravity where the diffeomorphism invariance of general relativity can be extended to a covariance under every permutation of spacetime events.
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Exact differential
In multivariate calculus, a differential is said to be exact or perfect, as contrasted with an inexact differential, if it is of the form dQ, for some differentiable function Q.
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Exchangeable random variables
In statistics, an exchangeable sequence of random variables (also sometimes interchangeable) is a sequence such that future observations behave like earlier observations.
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Exterior algebra
In mathematics, the exterior product or wedge product of vectors is an algebraic construction used in geometry to study areas, volumes, and their higher-dimensional analogs.
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External (mathematics)
The term external is useful for describing certain algebraic structures.
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External memory algorithm
In computing, external memory algorithms or out-of-core algorithms are algorithms that are designed to process data that is too large to fit into a computer's main memory at one time.
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Factorial
In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example, The value of 0! is 1, according to the convention for an empty product.
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Factorial moment measure
In probability and statistics, a factorial moment measure is a mathematical quantity, function or, more precisely, measure that is defined in relation to mathematical objects known as point processes, which are types of stochastic processes often used as mathematical models of physical phenomena representable as randomly positioned points in time, space or both.
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Factorial number system
In combinatorics, the factorial number system, also called factoradic, is a mixed radix numeral system adapted to numbering permutations.
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Falling and rising factorials
In mathematics, the falling factorial (sometimes called the descending factorial, falling sequential product, or lower factorial) is defined as The rising factorial (sometimes called the Pochhammer function, Pochhammer polynomial, ascending factorial, (A reprint of the 1950 edition by Chelsea Publishing Co.) rising sequential product, or upper factorial) is defined as The value of each is taken to be 1 (an empty product) when n.
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Fano plane
In finite geometry, the Fano plane (after Gino Fano) is the finite projective plane of order 2.
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Farthest-first traversal
In computational geometry, the farthest-first traversal of a bounded metric space is a sequence of points in the space, where the first point is selected arbitrarily and each successive point is as far as possible from the set of previously-selected points.
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Feedback arc set
In graph theory, a directed graph may contain directed cycles, a one-way loop of edges.
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Fialka
In cryptography, Fialka (M-125) is the name of a Cold War-era Soviet cipher machine.
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Filtration (mathematics)
In mathematics, a filtration \mathcal is an indexed set S_i of subobjects of a given algebraic structure S, with the index i running over some index set I that is a totally ordered set, subject to the condition that If the index i is the time parameter of some stochastic process, then the filtration can be interpreted as representing all historical but not future information available about the stochastic process, with the algebraic object S_i gaining in complexity with time.
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Finite group
In abstract algebra, a finite group is a mathematical group with a finite number of elements.
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Fisher–Yates shuffle
The Fisher–Yates shuffle is an algorithm for generating a random permutation of a finite sequence—in plain terms, the algorithm shuffles the sequence.
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Football pools
In the United Kingdom, the football pools, often referred to as "the pools", is a betting pool based on predicting the outcome of top-level association football matches taking place in the coming week.
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Function composition
In mathematics, function composition is the pointwise application of one function to the result of another to produce a third function.
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Functional principal component analysis
Functional principal component analysis (FPCA) is a statistical method for investigating the dominant modes of variation of functional data.
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Galois theory
In the field of algebra within mathematics, Galois theory, provides a connection between field theory and group theory.
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Gambler's fallacy
The gambler's fallacy, also known as the Monte Carlo fallacy or the fallacy of the maturity of chances, is the mistaken belief that, if something happens more frequently than normal during a given period, it will happen less frequently in the future.
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Gambling mathematics
The mathematics of gambling are a collection of probability applications encountered in games of chance and can be included in game theory.
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Gaussian integral
The Gaussian integral, also known as the Euler–Poisson integral, is the integral of the Gaussian function e−x2 over the entire real line.
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Gear Cube
The Gear Cube is a 3-D combination puzzle designed and created by Dutch puzzle maker Oskar van Deventer (based on an idea by Bram Cohen).
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Generative art
Generative art refers to art that in whole or in part has been created with the use of an autonomous system.
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Generative design
Generative design is an iterative design process that involves a program that will generate a certain number of outputs that meet certain constraints, and a designer that will fine tune the feasible region by changing minimal and maximal values of an interval in which a variable of the program meets the set of constraints, in order to reduce or augment the number of outputs to choose from.
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Generic programming
Generic programming is a style of computer programming in which algorithms are written in terms of types to-be-specified-later that are then instantiated when needed for specific types provided as parameters.
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Genocchi number
In mathematics, the Genocchi numbers Gn, named after Angelo Genocchi, are a sequence of integers that satisfy the relation \frac.
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Ghost Leg
Ghost Leg, known in Japan as or in Korea as Sadaritagi (사다리타기, literally "ladder climbing"), is a method of lottery designed to create random pairings between two sets of any number of things, as long as the number of elements in each set is the same.
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Gilbert–Shannon–Reeds model
In the mathematics of shuffling playing cards, the Gilbert–Shannon–Reeds model is a probability distribution on riffle shuffle permutations that has been reported to be a good match for experimentally observed outcomes of human shuffling, and that forms the basis for a recommendation that a deck of cards should be riffled seven times in order to thoroughly randomize it.
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Gilbreath shuffle
A Gilbreath shuffle is a way to shuffle a deck of cards, named after mathematician Norman L. Gilbreath (also known for Gilbreath's conjecture).
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GNU Scientific Library
The GNU Scientific Library (or GSL) is a software library for numerical computations in applied mathematics and science.
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Golomb–Dickman constant
In mathematics, the Golomb–Dickman constant arises in the theory of random permutations and in number theory.
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Grace–Walsh–Szegő theorem
In mathematics, the Grace–Walsh–Szegő coincidence theorem is a result named after John Hilton Grace, Joseph L. Walsh, and Gábor Szegő.
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Graded poset
In mathematics, in the branch of combinatorics, a graded poset is a partially ordered set (poset) P equipped with a rank function ρ from P to N satisfying the following two properties.
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Grandi's series
In mathematics, the infinite series 1 - 1 + 1 - 1 + \dotsb, also written \sum_^ (-1)^n is sometimes called Grandi's series, after Italian mathematician, philosopher, and priest Guido Grandi, who gave a memorable treatment of the series in 1703.
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Grandsire
Grandsire is one of the standard change ringing methods, which are methods of ringing church bells or handbells using a series of mathematical permutations rather than using a melody.
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Graph automorphism
In the mathematical field of graph theory, an automorphism of a graph is a form of symmetry in which the graph is mapped onto itself while preserving the edge–vertex connectivity.
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Graph canonization
In graph theory, a branch of mathematics, graph canonization is the problem finding a canonical form of a given graph G. A canonical form is a labeled graph Canon(G) that is isomorphic to G, such that every graph that is isomorphic to G has the same canonical form as G. Thus, from a solution to the graph canonization problem, one could also solve the problem of graph isomorphism: to test whether two graphs G and H are isomorphic, compute their canonical forms Canon(G) and Canon(H), and test whether these two canonical forms are identical.
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Graph coloring
In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints.
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Gray code
The reflected binary code (RBC), also known just as reflected binary (RB) or Gray code after Frank Gray, is an ordering of the binary numeral system such that two successive values differ in only one bit (binary digit).
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Grönwall's inequality
In mathematics, Grönwall's inequality (also called Grönwall's lemma or the Grönwall–Bellman inequality) allows one to bound a function that is known to satisfy a certain differential or integral inequality by the solution of the corresponding differential or integral equation.
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Grill (cryptology)
The grill method (metoda rusztu), in cryptology, was a method used chiefly early on, before the advent of the cyclometer, by the mathematician-cryptologists of the Polish Cipher Bureau (Biuro Szyfrów) in decrypting German Enigma machine ciphers.
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Group (mathematics)
In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element and that satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility.
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Group action
In mathematics, an action of a group is a formal way of interpreting the manner in which the elements of the group correspond to transformations of some space in a way that preserves the structure of that space.
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Group representation
In the mathematical field of representation theory, group representations describe abstract groups in terms of linear transformations of vector spaces; in particular, they can be used to represent group elements as matrices so that the group operation can be represented by matrix multiplication.
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Group theory
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.
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H4 polytope
In 4-dimensional geometry, there are 15 uniform polytopes with H4 symmetry.
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Haecceitism
In metaphysics, haecceitism is the perspective implied by the belief that entities can have haecceity or individual essence, "a set of principles which are essential to it and distinguish it from everything else." James Ladyman characterizes haecceitism as "the claim that worlds can differ solo numero, that worlds can differ de re whilst not differing de dicto, sometimes said, that worlds can differ solely by the permutation of individuals.".
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Hall's universal group
In algebra, Hall's universal group is a countable locally finite group, say U, which is uniquely characterized by the following properties.
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Haploview
Haploview is a commonly used bioinformatics software which is designed to analyze and visualize patterns of linkage disequilibrium (LD) in genetic data.
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Heap (mathematics)
In abstract algebra, a heap (sometimes also called a groud) is a mathematical generalization of a group.
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Heap's algorithm
Heap's algorithm generates all possible permutations of objects.
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Heinrich August Rothe
Heinrich August Rothe (1773–1842) was a German mathematician, a professor of mathematics at Erlangen.
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Held–Karp algorithm
The Held–Karp algorithm, also called Bellman–Held–Karp algorithm, is a dynamic programming algorithm proposed in 1962 independently by Bellman and by Held and Karp to solve the Traveling Salesman Problem (TSP).
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Heptellated 8-simplexes
In eight-dimensional geometry, a heptellated 8-simplex is a convex uniform 8-polytope, including 7th-order truncations (heptellation) from the regular 8-simplex.
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Hewitt–Savage zero–one law
The Hewitt–Savage zero–one law is a theorem in probability theory, similar to Kolmogorov's zero–one law and the Borel–Cantelli lemma, that specifies that a certain type of event will either almost surely happen or almost surely not happen.
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Higher-dimensional gamma matrices
In mathematical physics, higher-dimensional gamma matrices generalize to arbitrary dimension the four-dimensional Gamma matrices of Dirac, which are a mainstay of relativistic quantum mechanics.
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History of group theory
The history of group theory, a mathematical domain studying groups in their various forms, has evolved in various parallel threads.
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History of mathematical notation
The history of mathematical notation includes the commencement, progress, and cultural diffusion of mathematical symbols and the conflict of the methods of notation confronted in a notation's move to popularity or inconspicuousness.
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Hoffman–Singleton graph
In the mathematical field of graph theory, the Hoffman–Singleton graph is a 7-regular undirected graph with 50 vertices and 175 edges.
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Holomorph (mathematics)
In mathematics, especially in the area of algebra known as group theory, the holomorph of a group is a group which simultaneously contains (copies of) the group and its automorphism group.
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Homography
In projective geometry, a homography is an isomorphism of projective spaces, induced by an isomorphism of the vector spaces from which the projective spaces derive.
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HP 35s
The HP 35s (F2215A) is the latest in Hewlett-Packard's long line of non-graphing programmable scientific calculators.
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Hypercube graph
In graph theory, the hypercube graph is the graph formed from the vertices and edges of an -dimensional hypercube.
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Hypergraph
In mathematics, a hypergraph is a generalization of a graph in which an edge can join any number of vertices.
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Identical particles
Identical particles, also called indistinguishable or indiscernible particles, are particles that cannot be distinguished from one another, even in principle.
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In-place matrix transposition
In-place matrix transposition, also called in-situ matrix transposition, is the problem of transposing an N×M matrix in-place in computer memory, ideally with ''O''(1) (bounded) additional storage, or at most with additional storage much less than NM.
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Inclusion–exclusion principle
In combinatorics (combinatorial mathematics), the inclusion–exclusion principle is a counting technique which generalizes the familiar method of obtaining the number of elements in the union of two finite sets; symbolically expressed as where A and B are two finite sets and |S| indicates the cardinality of a set S (which may be considered as the number of elements of the set, if the set is finite).
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Income inequality metrics
Income inequality metrics or income distribution metrics are used by social scientists to measure the distribution of income, and economic inequality among the participants in a particular economy, such as that of a specific country or of the world in general.
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Incomplete gamma function
In mathematics, the upper incomplete gamma function and lower incomplete gamma function are types of special functions, which arise as solutions to various mathematical problems such as certain integrals.
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Independent and identically distributed random variables
In probability theory and statistics, a sequence or other collection of random variables is independent and identically distributed (i.i.d. or iid or IID) if each random variable has the same probability distribution as the others and all are mutually independent.
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Index of combinatorics articles
No description.
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Indicator value
Indicator value is a term that has been used in ecology for two different indices.
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Infinite conjugacy class property
In mathematics, a group is said to have the infinite conjugacy class property, or to be an icc group, if the conjugacy class of every group element but the identity is infinite.
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Information oriented software development
Information Oriented Software Development is a software development methodology focused on working with information inside a computer program as opposed to working with just data.
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Integer lattice
In mathematics, the n-dimensional integer lattice (or cubic lattice), denoted Zn, is the lattice in the Euclidean space Rn whose lattice points are ''n''-tuples of integers.
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Integral transform
In mathematics, an integral transform maps an equation from its original domain into another domain where it might be manipulated and solved much more easily than in the original domain.
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Interval exchange transformation
In mathematics, an interval exchange transformation is a kind of dynamical system that generalises circle rotation.
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Invariant theory
Invariant theory is a branch of abstract algebra dealing with actions of groups on algebraic varieties, such as vector spaces, from the point of view of their effect on functions.
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Inversion (discrete mathematics)
In computer science and discrete mathematics a sequence has an inversion where two of its elements are out of their natural order.
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Inversion (music)
There are inverted chords, inverted melodies, inverted intervals, and (in counterpoint) inverted voices.
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Involution (mathematics)
In mathematics, an involution, or an involutory function, is a function that is its own inverse, for all in the domain of.
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Joe Beevers
Joseph Charles "Joe" Beevers (born 9 December 1967 in Marylebone, London) is an English professional poker player and a member of The Hendon Mob.
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Jorge Luis Borges and mathematics
Jorge Luis Borges and mathematics concerns several modern mathematical concepts found in certain essays and short stories of Argentinian author Jorge Luis Borges (1899-1986), including concepts such as set theory, recursion, chaos theory, and infinite sequences, although Borges' strongest links to mathematics are through Georg Cantor's theory of infinite sets, outlined in "The Doctrine of Cycles" (La doctrina de los ciclos).
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Journal of Modern Applied Statistical Methods
The Journal of Modern Applied Statistical Methods is a biannual peer-reviewed open access journal.
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Jumble algorithm
Each clue in a Jumble word puzzle is a word that has been “jumbled” by permuting the letters of each word to make an anagram.
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Kakuro
Kakuro or Kakkuro (カックロ) is a kind of logic puzzle that is often referred to as a mathematical transliteration of the crossword.
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Karma in Jainism
Karma is the basic principle within an overarching psycho-cosmology in Jainism.
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Katalin Vesztergombi
Katalin L. Vesztergombi (born 1948) is a Hungarian mathematician known for her contributions to graph theory and discrete geometry.
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Kolakoski sequence
In mathematics, the Kolakoski sequence, sometimes also known as the Oldenburger-Kolakoski sequence, is an infinite sequence of symbols that is its own run-length encoding and the prototype for an infinite family of related sequences.
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Kolmogorov extension theorem
In mathematics, the Kolmogorov extension theorem (also known as Kolmogorov existence theorem or Kolmogorov consistency theorem) is a theorem that guarantees that a suitably "consistent" collection of finite-dimensional distributions will define a stochastic process.
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Kreuzspiel
Kreuzspiel (Crossplay) is a composition by Karlheinz Stockhausen written for oboe, bass clarinet, piano and four percussionists in 1951 (it was later revised for just three percussionists, along with other changes).
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Lady tasting tea
In the design of experiments in statistics, the lady tasting tea is a randomized experiment devised by Ronald Fisher and reported in his book The Design of Experiments (1935).
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Lai–Massey scheme
The Lai–Massey scheme is a cryptographic structure used in the design of block ciphers.
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Landau's function
In mathematics, Landau's function g(n), named after Edmund Landau, is defined for every natural number n to be the largest order of an element of the symmetric group Sn.
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Langford pairing
In combinatorial mathematics, a Langford pairing, also called a Langford sequence, is a permutation of the sequence of 2n numbers 1, 1, 2, 2,..., n, n in which the two ones are one unit apart, the two twos are two units apart, and more generally the two copies of each number k are k units apart.
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Laplace expansion
In linear algebra, the Laplace expansion, named after Pierre-Simon Laplace, also called cofactor expansion, is an expression for the determinant |B| of an n × n matrix B that is a weighted sum of the determinants of n sub-matrices of B, each of size (n−1) × (n−1).
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Large numbers
Large numbers are numbers that are significantly larger than those ordinarily used in everyday life, for instance in simple counting or in monetary transactions.
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Latin square
In combinatorics and in experimental design, a Latin square is an n × n array filled with n different symbols, each occurring exactly once in each row and exactly once in each column.
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Layered graph drawing
Layered graph drawing or hierarchical graph drawing is a type of graph drawing in which the vertices of a directed graph are drawn in horizontal rows or layers with the edges generally directed downwards.
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Learning to rank
Learning to rank.
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Lebedev quadrature
In numerical analysis, Lebedev quadrature, named after Vyacheslav Ivanovich Lebedev, is an approximation to the surface integral of a function over a three-dimensional sphere.
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Lehmer code
In mathematics and in particular in combinatorics, the Lehmer code is a particular way to encode each possible permutation of a sequence of n numbers.
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Leibniz formula for determinants
In algebra, the Leibniz formula, named in honor of Gottfried Leibniz, expresses the determinant of a square matrix in terms of permutations of the matrix elements.
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Levi-Civita symbol
In mathematics, particularly in linear algebra, tensor analysis, and differential geometry, the Levi-Civita symbol represents a collection of numbers; defined from the sign of a permutation of the natural numbers, for some positive integer.
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List of cycles
This is a list of recurring cycles.
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List of factorial and binomial topics
This is a list of factorial and binomial topics in mathematics.
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List of Greek and Latin roots in English/M
Category:Lists of words.
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List of group theory topics
No description.
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List of Latin words with English derivatives
This is a list of Latin words with derivatives in English (and other modern languages).
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List of logarithmic identities
In mathematics, there are many logarithmic identities.
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List of matrices
This page lists some important classes of matrices used in mathematics, science and engineering.
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List of patent claim types
This is a list of special types of claims that may be found in a patent or patent application.
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List of permutation topics
This is a list of topics on mathematical permutations.
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List of regular polytopes and compounds
This page lists the regular polytopes and regular polytope compounds in Euclidean, spherical and hyperbolic spaces.
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List of small groups
The following list in mathematics contains the finite groups of small order up to group isomorphism.
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List of terms relating to algorithms and data structures
The NIST Dictionary of Algorithms and Data Structures is a reference work maintained by the U.S. National Institute of Standards and Technology.
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Longest increasing subsequence
In computer science, the longest increasing subsequence problem is to find a subsequence of a given sequence in which the subsequence's elements are in sorted order, lowest to highest, and in which the subsequence is as long as possible.
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Loopless algorithm
In computational combinatorics, a loopless algorithm or loopless imperative algorithm is an imperative algorithm that generates successive combinatorial objects, such as partitions, permutations, and combinations, in constant time and the first object in linear time.
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Lubell–Yamamoto–Meshalkin inequality
In combinatorial mathematics, the Lubell–Yamamoto–Meshalkin inequality, more commonly known as the LYM inequality, is an inequality on the sizes of sets in a Sperner family, proved by,,, and.
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Lyndon word
In mathematics, in the areas of combinatorics and computer science, a Lyndon word is a nonempty string that is strictly smaller in lexicographic order than all of its rotations.
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Magic hypercube
In mathematics, a magic hypercube is the ''k''-dimensional generalization of magic squares, magic cubes and magic tesseracts; that is, a number of integers arranged in an n × n × n ×...
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Major index
In mathematics (and particularly in combinatorics), the major index of a permutation is the sum of the positions of the descents of the permutation.
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Majorization
In mathematics, majorization is a preorder on vectors of real numbers.
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Manin matrix
In mathematics, Manin matrices, named after Yuri Manin who introduced them around 1987–88, are a class of matrices with elements in a not-necessarily commutative ring, which in a certain sense behave like matrices whose elements commute.
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Marian Rejewski
Marian Adam Rejewski (16 August 1905 – 13 February 1980) was a Polish mathematician and cryptologist who reconstructed the Nazi German military Enigma cipher machine sight-unseen in 1932.
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Mathematical beauty
Mathematical beauty describes the notion that some mathematicians may derive aesthetic pleasure from their work, and from mathematics in general.
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Mathematical object
A mathematical object is an abstract object arising in mathematics.
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Mathematics education
In contemporary education, mathematics education is the practice of teaching and learning mathematics, along with the associated scholarly research.
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Mathematics, Form and Function
Mathematics, Form and Function is a survey of the whole of mathematics, including its origins and deep structure, by the American mathematician Saunders Mac Lane.
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Matrix (music)
In music, especially folk and popular music, a matrix is an element of variations which does not change.
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Max Frisch
Max Rudolf Frisch (15 May 1911 – 4 April 1991) was a Swiss playwright and novelist.
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Maxwell–Boltzmann statistics
In statistical mechanics, Maxwell–Boltzmann statistics describes the average distribution of non-interacting material particles over various energy states in thermal equilibrium, and is applicable when the temperature is high enough or the particle density is low enough to render quantum effects negligible.
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Möbius–Kantor configuration
In geometry, the Möbius–Kantor configuration is a configuration consisting of eight points and eight lines, with three points on each line and three lines through each point.
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Meander (mathematics)
In mathematics, a meander or closed meander is a self-avoiding closed curve which intersects a line a number of times.
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Mental poker
Mental poker is the common name for a set of cryptographic problems that concerns playing a fair game over distance without the need for a trusted third party.
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Method ringing
Method ringing (also known as scientific ringing) is a form of change ringing in which the ringers commit to memory the rules for generating each change of sequence, and pairs of bells are affected.
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Microarray analysis techniques
Microarray analysis techniques are used in interpreting the data generated from experiments on DNA, RNA, and protein microarrays, which allow researchers to investigate the expression state of a large number of genes - in many cases, an organism's entire genome - in a single experiment.
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Microsoft Analysis Services
Microsoft SQL Server Analysis Services, SSAS, is an online analytical processing (OLAP) and data mining tool in Microsoft SQL Server.
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Miklós Bóna
Miklós Bóna (born October 6, 1967, in Székesfehérvár) is an American mathematician of Hungarian origin.
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Mixed radix
Mixed radix numeral systems are non-standard positional numeral systems in which the numerical base varies from position to position.
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Modern Arabic mathematical notation
Modern Arabic mathematical notation is a mathematical notation based on the Arabic script, used especially at pre-university levels of education.
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Muirhead's inequality
In mathematics, Muirhead's inequality, named after Robert Franklin Muirhead, also known as the "bunching" method, generalizes the inequality of arithmetic and geometric means.
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Multi-party fair exchange protocol
In cryptography, a multi-party fair exchange protocol is protocol where parties accept to deliver an item if and only if they receive an item in return.
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Multilinear form
In abstract algebra and multilinear algebra, a multilinear form on V is a map of the type f: V^k \to K,where V is a vector space over the field K (or more generally, a module over a commutative ring), that is separately K-linear in each of its k arguments.
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Multinomial theorem
In mathematics, the multinomial theorem describes how to expand a power of a sum in terms of powers of the terms in that sum.
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Muneer Ahmad Rashid
Muneer Ahmad Rashid, PhD, D.Sc., PAS Gold Medal, FPAS (born 1934), also spelled as Munir Ahmad Rashid, is a Pakistani Mathematical Physicist and Emeritus Professor of Applied and Mathematical Physics at the Centre for Advanced Mathematics and Physics of the National University of Sciences and Technology.
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Natural computing
Natural computing,G.Rozenberg, T.Back, J.Kok, Editors, Handbook of Natural Computing, Springer Verlag, 2012A.Brabazon, M.O'Neill, S.McGarraghy.
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Necklace (combinatorics)
In combinatorics, a k-ary necklace of length n is an equivalence class of n-character strings over an alphabet of size k, taking all rotations as equivalent.
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New Data Seal
In cryptography, New Data Seal (NDS) is a block cipher that was designed at IBM in 1975, based on the Lucifer algorithm that became DES.
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No free lunch in search and optimization
In computational complexity and optimization the no free lunch theorem is a result that states that for certain types of mathematical problems, the computational cost of finding a solution, averaged over all problems in the class, is the same for any solution method.
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Nomos Alpha
Nomos Alpha (Νόμος α΄) is a piece for solo cello composed by Iannis Xenakis in 1965, commissioned by Radio Bremen for cellist Siegfried Palm, and dedicated to mathematicians Aristoxenus of Tarentum, Évariste Galois, and Felix Klein.
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Non-negative matrix factorization
Non-negative matrix factorization (NMF or NNMF), also non-negative matrix approximation is a group of algorithms in multivariate analysis and linear algebra where a matrix is factorized into (usually) two matrices and, with the property that all three matrices have no negative elements.
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NPR (disambiguation)
NPR (formerly National Public Radio) is a media organization that serves as a national syndicator to most public radio stations in the United States.
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Nuclear fuel cycle
The nuclear fuel cycle, also called nuclear fuel chain, is the progression of nuclear fuel through a series of differing stages.
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Object–verb–subject
In linguistic typology, object–verb–subject (OVS) or object–verb–agent (OVA) is a rare permutation of word order.
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Oblivious ram
An Oblivious RAM (ORAM) simulator is a compiler that transforms algorithms in such a way that the resulting algorithms preserve the input-output behavior of the original algorithm but the distribution of memory access pattern of the transformed algorithm is independent of the memory access pattern of the original algorithm.
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Optimization problem
In mathematics and computer science, an optimization problem is the problem of finding the best solution from all feasible solutions.
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Order
Order or ORDER may refer to.
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Order (mathematics)
Order in mathematics may refer to.
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Orientation (vector space)
In mathematics, orientation is a geometric notion that in two dimensions allows one to say when a cycle goes around clockwise or counterclockwise, and in three dimensions when a figure is left-handed or right-handed.
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Oriented matroid
An oriented matroid is a mathematical structure that abstracts the properties of directed graphs and of arrangements of vectors in a vector space over an ordered field (particularly for partially ordered vector spaces).
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Orthogonal array
In mathematics, in the area of combinatorial designs, an orthogonal array is a "table" (array) whose entries come from a fixed finite set of symbols (typically), arranged in such a way that there is an integer t so that for every selection of t columns of the table, all ordered t-tuples of the symbols, formed by taking the entries in each row restricted to these columns, appear the same number of times.
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Orthogonal array testing
Orthogonal array testing is a black box testing technique that is a systematic, statistical way of software testing.
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Outline of arithmetic
Arithmetic is an elementary branch of mathematics that is used by almost everyone for tasks ranging from simple day-to-day counting to advanced science and business calculations.
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Outline of discrete mathematics
Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous.
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Palindrome
A palindrome is a word, number, or other sequence of characters which reads the same backward as forward, such as madam or racecar.
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Pancake sorting
Pancake sorting is the colloquial term for the mathematical problem of sorting a disordered stack of pancakes in order of size when a spatula can be inserted at any point in the stack and used to flip all pancakes above it.
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Paracompact uniform honeycombs
In geometry, uniform honeycombs in hyperbolic space are tessellations of convex uniform polyhedron cells.
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Parastatistics
In quantum mechanics and statistical mechanics, parastatistics is one of several alternatives to the better known particle statistics models (Bose–Einstein statistics, Fermi–Dirac statistics and Maxwell–Boltzmann statistics).
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Parimutuel betting
Parimutuel betting (from the Pari Mutuel or mutual betting) is a betting system in which all bets of a particular type are placed together in a pool; taxes and the "house-take" or "vigorish" are removed, and payoff odds are calculated by sharing the pool among all winning bets.
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Parity of a permutation
In mathematics, when X is a finite set of at least two elements, the permutations of X (i.e. the bijective functions from X to X) fall into two classes of equal size: the even permutations and the odd permutations.
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Parry–Daniels map
In mathematics, the Parry–Daniels map is a function studied in the context of dynamical systems.
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Partial permutation
In combinatorial mathematics, a partial permutation, or sequence without repetition, on a finite set S is a bijection between two specified subsets of S. That is, it is defined by two subsets U and V of equal size, and a one-to-one mapping from U to V. Equivalently, it is a partial function on S that can be extended to a permutation.
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Path-ordering
In theoretical physics, path-ordering is the procedure (or a meta-operator \mathcal P) that orders a product of operators according to the value of a chosen parameter: Here p is a permutation that orders the parameters by value: For example.
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P′′
P′′ is a primitive computer programming language created by Corrado BöhmBöhm, C.: "On a family of Turing machines and the related programming language", ICC Bull.
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Pólya enumeration theorem
The Pólya enumeration theorem, also known as the Redfield–Pólya theorem, is a theorem in combinatorics that both follows from and ultimately generalizes Burnside's lemma on the number of orbits of a group action on a set.
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Pearson hashing
Pearson hashing is a hash function designed for fast execution on processors with 8-bit registers.
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Perm (disambiguation)
Perm or PERM may refer to.
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Permanent (mathematics)
In linear algebra, the permanent of a square matrix is a function of the matrix similar to the determinant.
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Permutable prime
A permutable prime, also known as anagrammatic prime, is a prime number which, in a given base, can have its digits' positions switched through any permutation and still be a prime number.
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Permutation
In mathematics, the notion of permutation relates to the act of arranging all the members of a set into some sequence or order, or if the set is already ordered, rearranging (reordering) its elements, a process called permuting.
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Permutation (disambiguation)
Permutation may refer to.
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Permutation (music)
In music, a permutation (order) of a set is any ordering of the elements of that set.
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Permutation automaton
In automata theory, a permutation automaton, or pure-group automaton, is a deterministic finite automaton such that each input symbol permutes the set of states.
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Permutation box
In cryptography, a permutation box (or P-box) is a method of bit-shuffling used to permute or transpose bits across S-boxes inputs, retaining diffusion while transposing.
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Permutation class
In the study of permutations and permutation patterns, a permutation class is a set C of permutations such that every pattern within a permutation in C is also in C. That is, it is a downset in the permutation pattern order.
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Permutation graph
In mathematics, a permutation graph is a graph whose vertices represent the elements of a permutation, and whose edges represent pairs of elements that are reversed by the permutation.
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Permutation group
In mathematics, a permutation group is a group G whose elements are permutations of a given set M and whose group operation is the composition of permutations in G (which are thought of as bijective functions from the set M to itself).
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Permutation matrix
\pi.
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Permutation model
In mathematical set theory, a permutation model is a model of set theory with atoms (ZFA) constructed using a group of permutations of the atoms.
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Permutation pattern
In combinatorial mathematics and theoretical computer science, a permutation pattern is a sub-permutation of a longer permutation.
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Permutation polynomial
In mathematics, a permutation polynomial (for a given ring) is a polynomial that acts as a permutation of the elements of the ring, i.e. the map x \mapsto g(x) is a bijection.
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Permutation representation
In mathematics, the term permutation representation of a (typically finite) group G can refer to either of two closely related notions: a representation of G as a group of permutations, or as a group of permutation matrices.
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Permuted congruential generator
A permuted congruential generator (PCG) is an pseudorandom number generation algorithm developed in 2014 which applies an output permutation function to improve the statistical properties of a modulo-2n linear congruential generator.
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Permutohedron
In mathematics, the permutohedron of order n (also spelled permutahedron) is an (n − 1)-dimensional polytope embedded in an n-dimensional space, the vertices of which are formed by permuting the coordinates of the vector (1, 2, 3,..., n).
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Pfaffian
In mathematics, the determinant of a skew-symmetric matrix can always be written as the square of a polynomial in the matrix entries, a polynomial with integer coefficients that only depend on the size of the matrix.
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Place-permutation action
In mathematics, there are two natural interpretations of the place-permutation action of symmetric groups, in which the group elements act on positions or places.
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Placebo-controlled study
Placebo-controlled studies are a way of testing a medical therapy in which, in addition to a group of subjects that receives the treatment to be evaluated, a separate control group receives a sham "placebo" treatment which is specifically designed to have no real effect.
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Plancherel measure
In mathematics, Plancherel measure is a measure defined on the set of irreducible unitary representations of a locally compact group G, that describes how the regular representation breaks up into irreducible unitary representations.
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Pocket Cube
The Pocket Cube (also known as the Mini Cube) is the 2×2×2 equivalent of a Rubik's Cube.
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Point-to-point transit
Point-to-point transit refers to a transportation system in which a plane, bus, or train travels directly to a destination, rather than going through a central hub.
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Poker probability
In poker, the probability of each type of 5-card hand can be computed by calculating the proportion of hands of that type among all possible hands.
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Portable, Extensible Toolkit for Scientific Computation
The Portable, Extensible Toolkit for Scientific Computation (PETSc, pronounced PET-see; the S is silent), is a suite of data structures and routines developed by Argonne National Laboratory for the scalable (parallel) solution of scientific applications modeled by partial differential equations.
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PQ tree
A PQ tree is a tree-based data structure that represents a family of permutations on a set of elements, discovered and named by Kellogg S. Booth and George S. Lueker in 1976.
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PRC200
PRC200-SS is an arylalkanolamine TRI being developed by the Mayo Clinic.
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Preorder
In mathematics, especially in order theory, a preorder or quasiorder is a binary relation that is reflexive and transitive.
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Price index
A price index (plural: “price indices” or “price indexes”) is a normalized average (typically a weighted average) of price relatives for a given class of goods or services in a given region, during a given interval of time.
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Primeval number
In mathematics, a primeval number is a natural number n for which the number of prime numbers which can be obtained by permuting some or all of its digits (in base 10) is larger than the number of primes obtainable in the same way for any smaller natural number.
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Professor's Cube
The Professor's Cube is a combination puzzle, a 5×5×5 version of the Rubik's Cube.
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Programming by permutation
Programming by permutation, sometimes called "programming by accident" or "by-try programming" or "shotgunning", is an approach to software development wherein a programming problem is solved by iteratively making small changes (permutations) and testing each change to see if it behaves as desired.
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Pseudorandom generator theorem
In computational complexity theory and cryptography, the existence of pseudorandom generators is related to the existence of one-way functions through a number of theorems, collectively referred to as the pseudorandom generator theorem.
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Pseudorandom permutation
In cryptography, a pseudorandom permutation (PRP) is a function that cannot be distinguished from a random permutation (that is, a permutation selected at random with uniform probability, from the family of all permutations on the function's domain) with practical effort.
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Punkte
Punkte (Points) is an orchestral composition by Karlheinz Stockhausen, given the work number ½ in his catalogue of works.
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Q-analog
In mathematics, a q-analog of a theorem, identity or expression is a generalization involving a new parameter q that returns the original theorem, identity or expression in the limit as.
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Q-Pochhammer symbol
In mathematics, in the area of combinatorics, a q-Pochhammer symbol, also called a q-shifted factorial, is a ''q''-analog of the Pochhammer symbol.
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Quantum field theory
In theoretical physics, quantum field theory (QFT) is the theoretical framework for constructing quantum mechanical models of subatomic particles in particle physics and quasiparticles in condensed matter physics.
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Quasi-set theory
Quasi-set theory is a formal mathematical theory for dealing with collections of indistinguishable objects, mainly motivated by the assumption that certain objects treated in quantum physics are indistinguishable and don't have individuality.
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Queue number
In mathematics, the queue number of a graph is a graph invariant defined analogously to stack number (book thickness) using first-in first-out (queue) orderings in place of last-in first-out (stack) orderings.
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Rabin cryptosystem
The Rabin cryptosystem is an asymmetric cryptographic technique, whose security, like that of RSA, is related to the difficulty of factorization.
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Random permutation
A random permutation is a random ordering of a set of objects, that is, a permutation-valued random variable.
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Rank correlation
In statistics, a rank correlation is any of several statistics that measure an ordinal association—the relationship between rankings of different ordinal variables or different rankings of the same variable, where a "ranking" is the assignment of the ordering labels "first", "second", "third", etc.
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Rank product
The rank product is a biologically motivated test for the detection of differentially expressed genes in replicated microarray experiments.
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RC4
In cryptography, RC4 (Rivest Cipher 4 also known as ARC4 or ARCFOUR meaning Alleged RC4, see below) is a stream cipher.
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Real coordinate space
In mathematics, real coordinate space of dimensions, written R (also written with blackboard bold) is a coordinate space that allows several (''n'') real variables to be treated as a single variable.
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Rearrangement inequality
In mathematics, the rearrangement inequality states that \le x_y_1 + \cdots + x_y_n \le x_1y_1 + \cdots + x_ny_n for every choice of real numbers and every permutation of x1,..., xn.
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Rebound attack
The rebound attack is a tool in the cryptanalysis of cryptographic hash functions.
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Rectified 9-simplexes
In nine-dimensional geometry, a rectified 9-simplex is a convex uniform 9-polytope, being a rectification of the regular 9-simplex.
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Recursive tree
In graph theory, a recursive tree (i.e., unordered tree) is a non-planar labeled rooted tree.
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Relation algebra
In mathematics and abstract algebra, a relation algebra is a residuated Boolean algebra expanded with an involution called converse, a unary operation.
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Relational quantum mechanics
Relational quantum mechanics (RQM) is an interpretation of quantum mechanics which treats the state of a quantum system as being observer-dependent, that is, the state is the relation between the observer and the system.
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Rencontres numbers
In combinatorial mathematics, the rencontres numbers are a triangular array of integers that enumerate permutations of the set with specified numbers of fixed points: in other words, partial derangements.
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Representation theory
Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures.
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Repunit
In recreational mathematics, a repunit is a number like 11, 111, or 1111 that contains only the digit 1 — a more specific type of repdigit.
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Residue-class-wise affine group
In mathematics, specifically in group theory, residue-class-wise affine groups are certain permutation groups acting on \mathbb (the integers), whose elements are bijective residue-class-wise affine mappings.
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Reversible cellular automaton
A reversible cellular automaton is a cellular automaton in which every configuration has a unique predecessor.
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Ricci calculus
In mathematics, Ricci calculus constitutes the rules of index notation and manipulation for tensors and tensor fields.
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Riemann series theorem
In mathematics, the Riemann series theorem (also called the Riemann rearrangement theorem), named after 19th-century German mathematician Bernhard Riemann, says that if an infinite series of real numbers is conditionally convergent, then its terms can be arranged in a permutation so that the new series converges to an arbitrary real number, or diverges.
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Riffle shuffle permutation
In the mathematics of permutations and the study of shuffling playing cards, a riffle shuffle permutation is one of the permutations of a set of n items that can be obtained by a single riffle shuffle, in which a sorted deck of n cards is cut into two packets and then the two packets are interleaved (e.g. by moving cards one at a time from the bottom of one or the other of the packets to the top of the sorted deck).
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Robinson–Schensted correspondence
In mathematics, the Robinson–Schensted correspondence is a bijective correspondence between permutations and pairs of standard Young tableaux of the same shape.
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Robinson–Schensted–Knuth correspondence
In mathematics, the Robinson–Schensted–Knuth correspondence, also referred to as the RSK correspondence or RSK algorithm, is a combinatorial bijection between matrices with non-negative integer entries and pairs of semistandard Young tableaux of equal shape, whose size equals the sum of the entries of.
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Robson Rotation
Robson Rotation is a method of arranging the names of candidates on ballot papers in single transferable vote elections so as to eliminate any influence of the so-called "donkey vote".
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Rook polynomial
In combinatorial mathematics, a rook polynomial is a generating polynomial of the number of ways to place non-attacking rooks on a board that looks like a checkerboard; that is, no two rooks may be in the same row or column.
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Root system
In mathematics, a root system is a configuration of vectors in a Euclidean space satisfying certain geometrical properties.
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Rotation matrix
In linear algebra, a rotation matrix is a matrix that is used to perform a rotation in Euclidean space.
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Round-robin DNS
Round Robin DNS is a technique of load distribution, load balancing, or fault-tolerance provisioning multiple, redundant Internet Protocol service hosts, e.g., Web server, FTP servers, by managing the Domain Name System's (DNS) responses to address requests from client computers according to an appropriate statistical model.
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Rounding
Rounding a numerical value means replacing it by another value that is approximately equal but has a shorter, simpler, or more explicit representation; for example, replacing $ with $, or the fraction 312/937 with 1/3, or the expression with.
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Row- and column-major order
In computing, row-major order and column-major order are methods for storing multidimensional arrays in linear storage such as random access memory.
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Rubik's Cube
Rubik's Cube is a 3-D combination puzzle invented in 1974 by Hungarian sculptor and professor of architecture Ernő Rubik.
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Rubik's Cube group
The Rubik’s Cube group is a group (G, \cdot) that represents the structure of the Rubik's Cube mechanical puzzle.
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Runcinated 5-cell
In four-dimensional geometry, a runcinated 5-cell is a convex uniform 4-polytope, being a runcination (a 3rd order truncation, up to face-planing) of the regular 5-cell.
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Runcinated 5-orthoplexes
In five-dimensional geometry, a runcinated 5-orthoplex is a convex uniform 5-polytope with 3rd order truncation (runcination) of the regular 5-orthoplex.
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Runcinated 5-simplexes
In six-dimensional geometry, a runcinated 5-simplex is a convex uniform 5-polytope with 3rd order truncations (Runcination) of the regular 5-simplex.
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Runcinated 6-cubes
In six-dimensional geometry, a runcinated 6-cube is a convex uniform 6-polytope with 3rd order truncations (runcination) of the regular 6-cube.
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Runcinated 6-orthoplexes
In six-dimensional geometry, a runcinated 6-orthplex is a convex uniform 6-polytope with 3rd order truncations (runcination) of the regular 6-orthoplex.
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Samuel Beckett
Samuel Barclay Beckett (13 April 1906 – 22 December 1989) was an Irish avant-garde novelist, playwright, theatre director, poet, and literary translator who lived in Paris for most of his adult life.
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Second quantization
Second quantization, also referred to as occupation number representation, is a formalism used to describe and analyze quantum many-body systems.
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Second-order cellular automaton
A second-order cellular automaton is a type of reversible cellular automaton (CA) invented by Edward Fredkin.
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Separable permutation
In combinatorial mathematics, a separable permutation is a permutation that can be obtained from the trivial permutation 1 by direct sums and skew sums.
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Separable polynomial
In mathematics, a polynomial P(X) over a given field K is separable if its roots are distinct in an algebraic closure of K, that is, the number of distinct roots is equal to the degree of the polynomial.
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Septic equation
In algebra, a septic equation is an equation of the form where.
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Sequent
In mathematical logic, a sequent is a very general kind of conditional assertion.
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Sesquilinear form
In mathematics, a sesquilinear form is a generalization of a bilinear form that, in turn, is a generalization of the concept of the dot product of Euclidean space.
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Set notation
Sets are fundamental objects in mathematics.
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Shape
A shape is the form of an object or its external boundary, outline, or external surface, as opposed to other properties such as color, texture or material composition.
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Shapley value
The Shapley value is a solution concept in cooperative game theory.
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Shen Kuo
Shen Kuo (1031–1095), courtesy name Cunzhong (存中) and pseudonym Mengqi (now usually given as Mengxi) Weng (夢溪翁),Yao (2003), 544.
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Shift matrix
In mathematics, a shift matrix is a binary matrix with ones only on the superdiagonal or subdiagonal, and zeroes elsewhere.
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Significance analysis of microarrays
Significance analysis of microarrays (SAM) is a statistical technique, established in 2001 by Virginia Tusher, Robert Tibshirani and Gilbert Chu, for determining whether changes in gene expression are statistically significant.
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Simple group
In mathematics, a simple group is a nontrivial group whose only normal subgroups are the trivial group and the group itself.
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Simulated annealing
Simulated annealing (SA) is a probabilistic technique for approximating the global optimum of a given function.
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Skew and direct sums of permutations
In combinatorics, the skew sum and direct sum of permutations are two operations to combine shorter permutations into longer ones.
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Skew-merged permutation
In the theory of permutation patterns, a skew-merged permutation is a permutation that can be partitioned into an increasing sequence and a decreasing sequence.
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Sort (C++)
sort is a generic function in the C++ Standard Library for doing comparison sorting.
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Sorting algorithm
In computer science, a sorting algorithm is an algorithm that puts elements of a list in a certain order.
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Spectr-H64
In cryptography, Spectr-H64 is a block cipher designed in 2001 by N. D. Goots, A. A. Moldovyan and N. A. Moldovyan.
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Speedcubing
Speedcubing (also known as speedsolving) is the sport involving solving a variety of twisty puzzles, the most famous being the Rubik's Cube, as quickly as possible.
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Spekkens toy model
The Spekkens toy model is a conceptually simple toy model introduced by Robert Spekkens in 2004, to argue in favour of the epistemic view of quantum mechanics.
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SPQR tree
In graph theory, a branch of mathematics, the triconnected components of a biconnected graph are a system of smaller graphs that describe all of the 2-vertex cuts in the graph.
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Stack-sortable permutation
In mathematics and computer science, a stack-sortable permutation (also called a tree permutation) is a permutation whose elements may be sorted by an algorithm whose internal storage is limited to a single stack data structure.
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Stanley symmetric function
In mathematics and especially in algebraic combinatorics, the Stanley symmetric functions are a family of symmetric polynomials introduced by in his study of the symmetric group of permutations.
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Steinhaus–Johnson–Trotter algorithm
The Steinhaus–Johnson–Trotter algorithm or Johnson–Trotter algorithm, also called plain changes, is an algorithm named after Hugo Steinhaus, Selmer M. Johnson and Hale F. Trotter that generates all of the permutations of n elements.
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Stericated 5-cubes
In five-dimensional geometry, a stericated 5-cube is a convex uniform 5-polytope with fourth-order truncations (sterication) of the regular 5-cube.
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Stirling number
In mathematics, Stirling numbers arise in a variety of analytic and combinatorial problems.
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Stirling numbers and exponential generating functions in symbolic combinatorics
The use of exponential generating functions (EGFs) to study the properties of Stirling numbers is a classical exercise in combinatorial mathematics and possibly the canonical example of how symbolic combinatorics is used.
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Stirling numbers of the first kind
In mathematics, especially in combinatorics, Stirling numbers of the first kind arise in the study of permutations.
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Stirling permutation
In combinatorial mathematics, a Stirling permutation of order k is a permutation of the multiset 1, 1, 2, 2,..., k, k (with two copies of each value from 1 to k) with the additional property that, for each value i appearing in the permutation, the values between the two copies of i are larger than i. For instance, the 15 Stirling permutations of order three are The number of Stirling permutations of order k is given by the double factorial (2k − 1)!!.
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Straight-five engine
The straight-five engine or inline-five engine is an internal combustion engine with five cylinders aligned in one row or plane, sharing a single engine block and crankcase.
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Substitution–permutation network
In cryptography, an SP-network, or substitution–permutation network (SPN), is a series of linked mathematical operations used in block cipher algorithms such as AES (Rijndael), 3-Way, Kuznyechik, PRESENT, SAFER, SHARK, and Square.
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Summation
In mathematics, summation (capital Greek sigma symbol: ∑) is the addition of a sequence of numbers; the result is their sum or total.
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Superpattern
In the mathematical study of permutations and permutation patterns, a superpattern is a permutation that contains all of the patterns of a given length.
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Sylvie Corteel
Sylvie Corteel is a French mathematician at the Centre national de la recherche scientifique and Paris Diderot University who is an editor-in-chief of the Journal of Combinatorial Theory, Series A. Her research concerns the enumerative combinatorics and algebraic combinatorics of permutations, tableaux, and partitions.
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Symmetric Boolean function
In mathematics, a symmetric Boolean function is a Boolean function whose value does not depend on the permutation of its input bits, i.e., it depends only on the number of ones in the input.
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Symmetric function
In mathematics, a symmetric function of n variables is one whose value given n arguments is the same no matter the order of the arguments.
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Symmetric game
In game theory, a symmetric game is a game where the payoffs for playing a particular strategy depend only on the other strategies employed, not on who is playing them.
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Symmetric group
In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the composition of functions.
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Symmetric inverse semigroup
In abstract algebra, the set of all partial bijections on a set X (one-to-one partial transformations) forms an inverse semigroup, called the symmetric inverse semigroup (actually a monoid) on X. The conventional notation for the symmetric inverse semigroup on a set X is \mathcal_X or \mathcal_X In general \mathcal_X is not commutative.
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Symmetric polynomial
In mathematics, a symmetric polynomial is a polynomial in variables, such that if any of the variables are interchanged, one obtains the same polynomial.
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Symmetric product (topology)
In algebraic topology, the symmetric product of a topological space consists of unordered -tuples of distinct points in.
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Symmetric tensor
In mathematics, a symmetric tensor is a tensor that is invariant under a permutation of its vector arguments: for every permutation σ of the symbols Alternatively, a symmetric tensor of order r represented in coordinates as a quantity with r indices satisfies The space of symmetric tensors of order r on a finite-dimensional vector space is naturally isomorphic to the dual of the space of homogeneous polynomials of degree r on V. Over fields of characteristic zero, the graded vector space of all symmetric tensors can be naturally identified with the symmetric algebra on V. A related concept is that of the antisymmetric tensor or alternating form.
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Symmetry in mathematics
Symmetry occurs not only in geometry, but also in other branches of mathematics.
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Symmetry operation
In the context of molecular symmetry, a symmetry operation is a permutation of atoms such that the molecule or crystal is transformed into a state indistinguishable from the starting state.
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Symplectic matrix
In mathematics, a symplectic matrix is a 2n×2n matrix M with real entries that satisfies the condition where MT denotes the transpose of M and Ω is a fixed 2n×2n nonsingular, skew-symmetric matrix.
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SymPy
SymPy is a Python library for symbolic computation.
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Szymanski's conjecture
In mathematics, Szymanski's conjecture, named after, states that every permutation on the n-dimensional doubly directed hypercube graph can be routed with edge-disjoint paths.
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Talpiot Tomb
The Talpiot Tomb (or Talpiyot Tomb) is a rock-cut tomb discovered in 1980 in the East Talpiot neighborhood, five kilometers (three miles) south of the Old City in East Jerusalem.
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Telephone number (mathematics)
In mathematics, the telephone numbers or the involution numbers are a sequence of integers that count the ways telephone lines can be connected to each other, where each line can be connected to at most one other line.
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Tensor product
In mathematics, the tensor product of two vector spaces and (over the same field) is itself a vector space, together with an operation of bilinear composition, denoted by, from ordered pairs in the Cartesian product into, in a way that generalizes the outer product.
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Tessellation
A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps.
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Tetrahedral symmetry
A regular tetrahedron, an example of a solid with full tetrahedral symmetry A regular tetrahedron has 12 rotational (or orientation-preserving) symmetries, and a symmetry order of 24 including transformations that combine a reflection and a rotation.
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The Art of Computer Programming
The Art of Computer Programming (sometimes known by its initials TAOCP) is a comprehensive monograph written by Donald Knuth that covers many kinds of programming algorithms and their analysis.
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The Computer Language Benchmarks Game
The Computer Language Benchmarks Game (formerly called The Great Computer Language Shootout) is a free software project for comparing how a given subset of simple algorithms can be implemented in various popular programming languages.
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The Engine
The Engine is a fictional device described in Gulliver's Travels by Jonathan Swift in 1726.
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The Library of Babel
"The Library of Babel" (La biblioteca de Babel) is a short story by Argentine author and librarian Jorge Luis Borges (1899–1986), conceiving of a universe in the form of a vast library containing all possible 410-page books of a certain format and character set.
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The Number Devil
The Number Devil: A Mathematical Adventure (Der Zahlenteufel.) is a book for children and young adults that explores mathematics.
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The Prisoner of Benda
"The Prisoner of Benda" is the 10th episode of the sixth season of the animated sitcom Futurama.
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The Schoolmaster's Assistant, Being a Compendium of Arithmetic both Practical and Theoretical
The Schoolmaster's Assistant, Being a Compendium of Arithmetic both Practical and Theoretical was an early and popular English arithmetic textbook, written by Thomas Dilworth and first published in England in 1743.
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Three-letter acronym
A three-letter acronym (TLA), or three-letter abbreviation, is an abbreviation, specifically an acronym, alphabetism, or initialism, consisting of three letters.
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Timeline of algebra
A timeline of key algebraic developments are as follows.
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Timeline of geometry
A timeline of algebra and geometry.
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Timeline of mathematics
This is a timeline of pure and applied mathematics history.
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Timeline of numerals and arithmetic
A timeline of numerals and arithmetic.
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Tompkins–Paige algorithm
The Tompkins–Paige algorithm is a computer algorithm for generating all permutations of a finite set of objects.
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Tracy–Widom distribution
The Tracy–Widom distribution, introduced by, is the probability distribution of the normalized largest eigenvalue of a random Hermitian matrix.
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Translation surface
In mathematics a translation surface is a surface obtained from identifying the sides of a polygon in the Euclidean plane by translations.
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Transpose
In linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal, that is it switches the row and column indices of the matrix by producing another matrix denoted as AT (also written A′, Atr, tA or At).
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Transposition cipher
In cryptography, a transposition cipher is a method of encryption by which the positions held by units of plaintext (which are commonly characters or groups of characters) are shifted according to a regular system, so that the ciphertext constitutes a permutation of the plaintext.
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Travelling salesman problem
The travelling salesman problem (TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city and returns to the origin city?" It is an NP-hard problem in combinatorial optimization, important in operations research and theoretical computer science.
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Truncated 5-orthoplexes
In six-dimensional geometry, a truncated 5-orthoplex is a convex uniform 5-polytope, being a truncation of the regular 5-orthoplex.
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Truncated 6-orthoplexes
In six-dimensional geometry, a truncated 6-orthoplex is a convex uniform 6-polytope, being a truncation of the regular 6-orthoplex.
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Truncated 7-cubes
In seven-dimensional geometry, a truncated 7-cube is a convex uniform 7-polytope, being a truncation of the regular 7-cube.
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Truncated 7-orthoplexes
In seven-dimensional geometry, a truncated 7-orthoplex is a convex uniform 7-polytope, being a truncation of the regular 7-orthoplex.
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Truncated 8-cubes
In eight-dimensional geometry, a truncated 8-cube is a convex uniform 8-polytope, being a truncation of the regular 8-cube.
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Truncated 8-orthoplexes
In eight-dimensional geometry, a truncated 8-orthoplex is a convex uniform 8-polytope, being a truncation of the regular 8-orthoplex.
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Truncated cuboctahedron
In geometry, the truncated cuboctahedron is an Archimedean solid, named by Kepler as a truncation of a cuboctahedron.
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Truncated dodecadodecahedron
In geometry, the truncated dodecadodecahedron is a nonconvex uniform polyhedron, indexed as U59.
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Truncated octahedron
In geometry, the truncated octahedron is an Archimedean solid.
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Truth value
In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth.
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Turbo code
In information theory, turbo codes (originally in French Turbocodes) are a class of high-performance forward error correction (FEC) codes developed around 1990–91 (but first published in 1993), which were the first practical codes to closely approach the channel capacity, a theoretical maximum for the code rate at which reliable communication is still possible given a specific noise level.
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Twelvefold way
In combinatorics, the twelvefold way is a systematic classification of 12 related enumerative problems concerning two finite sets, which include the classical problems of counting permutations, combinations, multisets, and partitions either of a set or of a number.
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Unconditional convergence
Unconditional convergence is a topological property (convergence) related to an algebraic object (sum).
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Unified neutral theory of biodiversity
The unified neutral theory of biodiversity and biogeography (here "Unified Theory" or "UNTB") is a hypothesis and the title of a monograph by ecologist Stephen Hubbell.
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Uniform 6-polytope
In six-dimensional geometry, a uniform polypeton (or uniform 6-polytope) is a six-dimensional uniform polytope.
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Uniform honeycombs in hyperbolic space
In hyperbolic geometry, a uniform honeycomb in hyperbolic space is a uniform tessellation of uniform polyhedral cells.
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Uniform matroid
In mathematics, a uniform matroid is a matroid in which every permutation of the elements is a symmetry.
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Unique games conjecture
In computational complexity theory, the unique games conjecture is a conjecture made by Subhash Khot in 2002.
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Uniquely colorable graph
In graph theory, a uniquely colorable graph is a k-chromatic graph that has only one possible (proper) ''k''-coloring up to permutation of the colors.
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Universal point set
In graph drawing, a universal point set of order n is a set S of points in the Euclidean plane with the property that every n-vertex planar graph has a straight-line drawing in which the vertices are all placed at points of S.
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Up to
In mathematics, the phrase up to appears in discussions about the elements of a set (say S), and the conditions under which subsets of those elements may be considered equivalent.
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V-Cube 6
The V-Cube 6 is a 6×6×6 version of Rubik's Cube.
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V-Cube 8
The V-Cube 8 is an 8×8×8 version of Rubik's Cube.
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Variably Modified Permutation Composition
VMPC (Variably Modified Permutation Composition) is a stream cipher similar to the well known and popular cipher RC4 designed by Ron Rivest.
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Vendor lock-in
In economics, vendor lock-in, also known as proprietary lock-in or customer lock-in, makes a customer dependent on a vendor for products and services, unable to use another vendor without substantial switching costs.
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Verbal arithmetic
Verbal arithmetic, also known as alphametics, cryptarithmetic, cryptarithm or word addition, is a type of mathematical game consisting of a mathematical equation among unknown numbers, whose digits are represented by letters.
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Verhoeff algorithm
The Verhoeff algorithm is a checksum formula for error detection developed by the Dutch mathematician Jacobus Verhoeff and was first published in 1969.
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Vexillary permutation
In mathematics, a vexillary permutation is a permutation μ of the positive integers containing no subpermutation isomorphic to the permutation (2143); in other words, there do not exist four numbers i.
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Virial coefficient
Virial coefficients B_i appear as coefficients in the virial expansion of the pressure of a many-particle system in powers of the density, providing systematic corrections to the ideal gas law.
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Vogel plane
In mathematics, the Vogel plane is a method of parameterizing simple Lie algebras by eigenvalues α, β, γ of the Casimir operator on the symmetric square of the Lie algebra, which gives a point (α: β: γ) of P2/S3, the projective plane P2 divided out by the symmetric group S3 of permutations of coordinates.
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Volumetric display
A volumetric display device is a graphic display device that forms a visual representation of an object in three physical dimensions, as opposed to the planar image of traditional screens that simulate depth through a number of different visual effects.
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Von Neumann–Bernays–Gödel set theory
In the foundations of mathematics, von Neumann–Bernays–Gödel set theory (NBG) is an axiomatic set theory that is a conservative extension of Zermelo–Fraenkel set theory (ZFC).
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Walsh matrix
In mathematics, a Walsh matrix is a specific square matrix of dimensions 2^n, where n are some particular natural number.
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Westminster Quarters
The Westminster Quarters is the most common name for a clock chime melody used by a set of four bells to chime on each quarter-hour.
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Wilf equivalence
In the study of permutations and permutation patterns, Wilf equivalence is an equivalence relation on permutation classes.
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William A. Veech
William A. Veech was the Edgar O. Lovett Professor of Mathematics at Rice University, Rice University, retrieved 2015-03-01.
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Writing system
A writing system is any conventional method of visually representing verbal communication.
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X Window System core protocol
The X Window System core protocolRobert W. Scheifler and James Gettys: X Window System: Core and extension protocols, X version 11, releases 6 and 6.1, Digital Press 1996, RFC 1013Grant Edwards.
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Xenocrates
Xenocrates (Ξενοκράτης; c. 396/5314/3 BC) of Chalcedon was a Greek philosopher, mathematician, and leader (scholarch) of the Platonic Academy from 339/8 to 314/3 BC.
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Yanagisawa Wind Instruments
Yanagisawa Wind Instruments is a Japanese woodwind company known for its range of professional grade saxophones.
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Yoneda lemma
In mathematics, specifically in category theory, the Yoneda lemma is an abstract result on functors of the type morphisms into a fixed object.
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Zolotarev's lemma
In number theory, Zolotarev's lemma states that the Legendre symbol for an integer a modulo an odd prime number p, where p does not divide a, can be computed as the sign of a permutation: where ε denotes the signature of a permutation and πa is the permutation of the nonzero residue classes mod p induced by multiplication by a. For example, take a.
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100 prisoners problem
The 100 prisoners problem is a mathematical problem in probability theory and combinatorics.
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120-cell
In geometry, the 120-cell is the convex regular 4-polytope with Schläfli symbol.
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163 (number)
163 (one hundred sixty-three) is the natural number following 162 and preceding 164.
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223 (number)
223 (two hundred twenty-three) is the natural number between 222 and 224.
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225 (number)
225 (two hundred twenty-five) is the natural number following 224 and preceding 226.
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226 (number)
226 (two hundred twenty-six) is the natural number following 225 and preceding 227.
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24-cell
In geometry, the 24-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol.
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3
3 (three) is a number, numeral, and glyph.
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3D4
In mathematics, the Steinberg triality groups of type 3D4 form a family of Steinberg or twisted Chevalley groups.
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4 21 polytope
In 8-dimensional geometry, the 421 is a semiregular uniform 8-polytope, constructed within the symmetry of the E8 group.
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4D vector
In computer science, a 4D vector is a 4-component vector data type.
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5040 (number)
5040 is a factorial (7!) and one less than a square, making (7, 71) a Brown number pair, a superior highly composite number, a colossally abundant number, and the number of permutations of 4 items out of 10 choices (10 × 9 × 8 × 7.
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Arrangement number, Calculating permutations, Circular notation, Cycle decomposition (group theory), Cycle notation, Cycle representation, Cyclic notation, Disposition (math), Identity permutation, K-permutation, NPr, Next permutation, One-line notation, Permutation algorithms, Permutations, Permute, Permuter, Permutes, Permuting.
References
[1] https://en.wikipedia.org/wiki/Permutation
