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79 relations: American Mathematical Society, Applied Probability Trust, Argumentum a fortiori, Associahedron, Associative property, Belgium, Bell number, Bertrand's ballot theorem, Bijective proof, Binary operation, Binary tree, Binomial coefficient, Binomial transform, Bracket, Cambridge University Press, Catalan's triangle, China, Combinatorics, Convex polygon, Coxeter group, Cumulant, Désiré André, Determinant, Double Mersenne number, Dyck language, Enumeration, Eugène Charles Catalan, Free probability, Fuss–Catalan number, Generating function, Hankel matrix, Hausdorff moment problem, Integer, Ira Gessel, Johann Andreas Segner, John Horton Conway, Lattice path, Leonhard Euler, Limit of a function, Line segment, List of factorial and binomial topics, Lobb number, Mathematical induction, Mathematician, Minggatu, Narayana number, Natural number, Noncrossing partition, Orthogonal polynomials, Permutation, ..., Permutation pattern, Polygon triangulation, Random matrix, Recurrence relation, Recursion, Richard K. Guy, Richard P. Stanley, Root system, Schröder–Hipparchus number, Semiorder, Sequence, Sergey Fomin, Stack (abstract data type), Stack-sortable permutation, Stirling's approximation, String (computer science), Tamari lattice, The Mathematical Gazette, Tower of Hanoi, Tree (graph theory), Triangle, Wedderburn–Etherington number, Wigner semicircle distribution, 1, 132 (number), 14 (number), 2, 42 (number), 5. Expand index (29 more) »
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.
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Applied Probability Trust
The Applied Probability Trust is a UK-based non-profit foundation for study and research in the mathematical sciences, founded in 1964 and based at the University of Sheffield.
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Argumentum a fortiori
Argumentum a fortiori (Latin: "from a/the stronger ") is a form of argumentation which draws upon existing confidence in a proposition to argue in favor of a second proposition that is held to be implicit in the first.
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Associahedron
In mathematics, an associahedron Kn is an (n − 2)-dimensional convex polytope in which each vertex corresponds to a way of correctly inserting opening and closing parentheses in a word of n letters and the edges correspond to single application of the associativity rule.
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Associative property
In mathematics, the associative property is a property of some binary operations.
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Belgium
Belgium, officially the Kingdom of Belgium, is a country in Western Europe bordered by France, the Netherlands, Germany and Luxembourg.
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Bell number
In combinatorial mathematics, the Bell numbers count the possible partitions of a set.
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Bertrand's ballot theorem
In combinatorics, Bertrand's ballot problem is the question: "In an election where candidate A receives p votes and candidate B receives q votes with p > q, what is the probability that A will be strictly ahead of B throughout the count?" The answer is The result was first published by W. A. Whitworth in 1878, but is named after Joseph Louis François Bertrand who rediscovered it in 1887.
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Bijective proof
In combinatorics, bijective proof is a proof technique that finds a bijective function f: A → B between two finite sets A and B, or a size-preserving bijective function between two combinatorial classes, thus proving that they have the same number of elements, |A|.
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Binary operation
In mathematics, a binary operation on a set is a calculation that combines two elements of the set (called operands) to produce another element of the set.
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Binary tree
In computer science, a binary tree is a tree data structure in which each node has at most two children, which are referred to as the and the.
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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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Binomial transform
In combinatorics, the binomial transform is a sequence transformation (i.e., a transform of a sequence) that computes its forward differences.
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Bracket
A bracket is a tall punctuation mark typically used in matched pairs within text, to set apart or interject other text.
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Cambridge University Press
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
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Catalan's triangle
In combinatorial mathematics, Catalan's triangle is a number triangle whose entries C(n,k) give the number of strings consisting of n X's and k Y's such that no initial segment of the string has more Y's than X's.
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China
China, officially the People's Republic of China (PRC), is a unitary one-party sovereign state in East Asia and the world's most populous country, with a population of around /1e9 round 3 billion.
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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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Convex polygon
A convex polygon is a simple polygon (not self-intersecting) in which no line segment between two points on the boundary ever goes outside the polygon.
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Coxeter group
In mathematics, a Coxeter group, named after H. S. M. Coxeter, is an abstract group that admits a formal description in terms of reflections (or kaleidoscopic mirrors).
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Cumulant
In probability theory and statistics, the cumulants of a probability distribution are a set of quantities that provide an alternative to the moments of the distribution.
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Désiré André
Désiré André (André Antoine Désiré) (March 29, 1840, Lyon – September 12, 1917, Paris) was a French mathematician, best known for his work on Catalan numbers and alternating permutations.
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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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Double Mersenne number
In mathematics, a double Mersenne number is a Mersenne number of the form where p is a prime exponent.
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Dyck language
In the theory of formal languages of computer science, mathematics, and linguistics, a Dyck word is a balanced string of square brackets.
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Enumeration
An enumeration is a complete, ordered listing of all the items in a collection.
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Eugène Charles Catalan
Eugène Charles Catalan (30 May 1814 – 14 February 1894) was a French and Belgian mathematician who worked on continued fractions, descriptive geometry, number theory and combinatorics.
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Free probability
Free probability is a mathematical theory that studies non-commutative random variables.
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Fuss–Catalan number
In combinatorial mathematics and statistics, the Fuss–Catalan numbers are numbers of the form They are named after N. I. Fuss and Eugène Charles Catalan.
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Generating function
In mathematics, a generating function is a way of encoding an infinite sequence of numbers (an) by treating them as the coefficients of a power series.
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Hankel matrix
In linear algebra, a Hankel matrix (or catalecticant matrix), named after Hermann Hankel, is a square matrix in which each ascending skew-diagonal from left to right is constant, e.g.: a & b & c & d & e \\ b & c & d & e & f \\ c & d & e & f & g \\ d & e & f & g & h \\ e & f & g & h & i \\ \end.
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Hausdorff moment problem
In mathematics, the Hausdorff moment problem, named after Felix Hausdorff, asks for necessary and sufficient conditions that a given sequence be the sequence of moments of some Borel measure μ supported on the closed unit interval.
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Integer
An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").
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Ira Gessel
Ira Martin Gessel (born 9 April 1951 in Philadelphia, Pennsylvania) is an American mathematician, known for his work in combinatorics.
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Johann Andreas Segner
Johann Segner (János András Segner, Johann Andreas von Segner, Ján Andrej Segner, Iohannes Andreas de Segner; October 9, 1704 – October 5, 1777) was a Hungarian scientist.
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John Horton Conway
John Horton Conway FRS (born 26 December 1937) is an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory.
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Lattice path
In combinatorics, a lattice path L in \mathbb^d of length k with steps in S is a sequence v_0, v_1, \ldots, v_k \in \mathbb^d such that each consecutive difference v_i - v_ lies in S. A lattice path may lie in any lattice in \mathbb^d, but the integer lattice \mathbb^d is most commonly used.
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Leonhard Euler
Leonhard Euler (Swiss Standard German:; German Standard German:; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory.
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Limit of a function
Although the function (sin x)/x is not defined at zero, as x becomes closer and closer to zero, (sin x)/x becomes arbitrarily close to 1.
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Line segment
In geometry, a line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoints.
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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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Lobb number
In combinatorial mathematics, the Lobb number Lm,n counts the number of ways that n + m open parentheses and n − m close parentheses can be arranged to form the start of a valid sequence of balanced parentheses.
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Mathematical induction
Mathematical induction is a mathematical proof technique.
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Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.
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Minggatu
Minggatu (Mongolian script:;, c.1692-c. 1763), full name Sharabiin Myangat (Шаравын Мянгат) was a Mongolian astronomer, mathematician, and topographic scientist at the Qing court.
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Narayana number
In combinatorics, the Narayana numbers N(n, k), n.
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Natural number
In mathematics, the natural numbers are those used for counting (as in "there are six coins on the table") and ordering (as in "this is the third largest city in the country").
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Noncrossing partition
In combinatorial mathematics, the topic of noncrossing partitions has assumed some importance because of (among other things) its application to the theory of free probability.
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Orthogonal polynomials
In mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonal to each other under some inner product.
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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 pattern
In combinatorial mathematics and theoretical computer science, a permutation pattern is a sub-permutation of a longer permutation.
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Polygon triangulation
In computational geometry, polygon triangulation is the decomposition of a polygonal area (simple polygon) P into a set of triangles, Chapter 3: Polygon Triangulation: pp.45–61.
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Random matrix
In probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all elements are random variables.
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Recurrence relation
In mathematics, a recurrence relation is an equation that recursively defines a sequence or multidimensional array of values, once one or more initial terms are given: each further term of the sequence or array is defined as a function of the preceding terms.
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Recursion
Recursion occurs when a thing is defined in terms of itself or of its type.
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Richard K. Guy
Richard Kenneth Guy (born 30 September 1916) is a British mathematician, professor emeritus in the Department of Mathematics at the University of Calgary.
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Richard P. Stanley
Richard Peter Stanley (born June 23, 1944 in New York City, New York) is the Norman Levinson Professor of Applied Mathematics at the Massachusetts Institute of Technology, in Cambridge, Massachusetts.
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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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Schröder–Hipparchus number
In number theory, the Schröder–Hipparchus numbers form an integer sequence that can be used to count the number of plane trees with a given set of leaves, the number of ways of inserting parentheses into a sequence, and the number of ways of dissecting a convex polygon into smaller polygons by inserting diagonals.
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Semiorder
In order theory, a branch of mathematics, a semiorder is a type of ordering that may be determined for a set of items with numerical scores by declaring two items to be incomparable when their scores are within a given margin of error of each other, and by using the numerical comparison of their scores when those scores are sufficiently far apart.
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Sequence
In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed.
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Sergey Fomin
Sergey Vladimirovich Fomin (Сергей Владимирович Фомин) (born 16 February 1958 in Saint Petersburg, Russia) is a Russian American mathematician who has made important contributions in combinatorics and its relations with algebra, geometry, and representation theory.
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Stack (abstract data type)
In computer science, a stack is an abstract data type that serves as a collection of elements, with two principal operations.
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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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Stirling's approximation
In mathematics, Stirling's approximation (or Stirling's formula) is an approximation for factorials.
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String (computer science)
In computer programming, a string is traditionally a sequence of characters, either as a literal constant or as some kind of variable.
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Tamari lattice
In mathematics, a Tamari lattice, introduced by, is a partially ordered set in which the elements consist of different ways of grouping a sequence of objects into pairs using parentheses; for instance, for a sequence of four objects abcd, the five possible groupings are ((ab)c)d, (ab)(cd), (a(bc))d, a((bc)d), and a(b(cd)).
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The Mathematical Gazette
The Mathematical Gazette is an academic journal of mathematics education, published three times yearly, that publishes "articles about the teaching and learning of mathematics with a focus on the 15–20 age range and expositions of attractive areas of mathematics." It was established in 1894 by Edward Mann Langley as the successor to the Reports of the Association for the Improvement of Geometrical Teaching.
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Tower of Hanoi
The Tower of Hanoi (also called the Tower of Brahma or Lucas' Tower and sometimes pluralized) is a mathematical game or puzzle.
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Tree (graph theory)
In mathematics, and more specifically in graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path.
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Triangle
A triangle is a polygon with three edges and three vertices.
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Wedderburn–Etherington number
The Wedderburn–Etherington numbers are an integer sequence named for Ivor Malcolm Haddon Etherington.
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Wigner semicircle distribution
The Wigner semicircle distribution, named after the physicist Eugene Wigner, is the probability distribution supported on the interval the graph of whose probability density function f is a semicircle of radius R centered at (0, 0) and then suitably normalized (so that it is really a semi-ellipse): for −R ≤ x ≤ R, and f(x).
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1
1 (one, also called unit, unity, and (multiplicative) identity) is a number, numeral, and glyph.
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132 (number)
132 (one hundred thirty-two) is the natural number following 131 and preceding 133.
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14 (number)
14 (fourteen) is a natural number following 13 and succeeded by 15.
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2
2 (two) is a number, numeral, and glyph.
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42 (number)
42 (forty-two) is the natural number that succeeds 41 and precedes 43.
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5
5 (five) is a number, numeral, and glyph.
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Catalan Numbers, Catalan numbers, Catalan sequence, Catalan's problem, Dyck path, Quadruple factorial, Segner number, Segner numbers.
References
[1] https://en.wikipedia.org/wiki/Catalan_number
