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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. 

## Abraham ibn Ezra

Abraham ben Meir Ibn Ezra (אַבְרָהָם אִבְּן עֶזְרָא or ראב"ע; ابن عزرا; also known as Abenezra or Aben Ezra, 1089–c.1167) was one of the most distinguished Jewish biblical commentators and philosophers of the Middle Ages.

## Abstract algebra

In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures.

In number theory, the specialty additive number theory studies subsets of integers and their behavior under addition.

## Algebra

Algebra (from Arabic "al-jabr", literally meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis.

## Algebraic combinatorics

Algebraic combinatorics is an area of mathematics that employs methods of abstract algebra, notably group theory and representation theory, in various combinatorial contexts and, conversely, applies combinatorial techniques to problems in algebra.

## Algebraic topology

Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces.

## Analysis

Analysis is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it.

## Analysis of algorithms

In computer science, the analysis of algorithms is the determination of the computational complexity of algorithms, that is the amount of time, storage and/or other resources necessary to execute them.

## Analytic number theory

In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers.

## Ancient Greece

Ancient Greece was a civilization belonging to a period of Greek history from the Greek Dark Ages of the 13th–9th centuries BC to the end of antiquity (AD 600).

## Ancient history

Ancient history is the aggregate of past events, "History" from the beginning of recorded human history and extending as far as the Early Middle Ages or the post-classical history.

## Archimedes

Archimedes of Syracuse (Ἀρχιμήδης) was a Greek mathematician, physicist, engineer, inventor, and astronomer.

## Associahedron

In mathematics, an associahedron Kn is an (n &minus; 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.

## Astronomer

An astronomer is a scientist in the field of astronomy who concentrates their studies on a specific question or field outside the scope of Earth.

## Asymptotic analysis

In mathematical analysis, asymptotic analysis, also known as asymptotics, is a method of describing limiting behavior.

## Automata theory

Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them.

## 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|.

## Binomial coefficient

In mathematics, any of the positive integers that occurs as a coefficient in the binomial theorem is a binomial coefficient.

## Birkhoff polytope

The Birkhoff polytope Bn, also called the assignment polytope, the polytope of doubly stochastic matrices, or the perfect matching polytope of the complete bipartite graph K_, is the convex polytope in RN (where N.

## Blaise Pascal

Blaise Pascal (19 June 1623 – 19 August 1662) was a French mathematician, physicist, inventor, writer and Catholic theologian.

## Block design

In combinatorial mathematics, a block design is a set together with a family of subsets (repeated subsets are allowed at times) whose members are chosen to satisfy some set of properties that are deemed useful for a particular application.

## Boolean algebra (structure)

In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice.

## Cambridge University Press

Cambridge University Press (CUP) is the publishing business of the University of Cambridge.

## Campanology

Campanology (from Late Latin campana, "bell"; and Greek -λογία, -logia) is the study of bells.

## 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.

## Cauchy's theorem (geometry)

Cauchy's theorem is a theorem in geometry, named after Augustin Cauchy.

## Cayley graph

In mathematics, a Cayley graph, also known as a Cayley colour graph, Cayley diagram, group diagram, or colour group is a graph that encodes the abstract structure of a group.

## Chomsky hierarchy

In the formal languages of computer science and linguistics, the Chomsky hierarchy (occasionally referred to as Chomsky–Schützenberger hierarchy) is a containment hierarchy of classes of formal grammars.

## Chromatic polynomial

The chromatic polynomial is a graph polynomial studied in algebraic graph theory, a branch of mathematics.

## Chrysippus

Chrysippus of Soli (Χρύσιππος ὁ Σολεύς, Chrysippos ho Soleus) was a Greek Stoic philosopher.

## Classification of finite simple groups

In mathematics, the classification of the finite simple groups is a theorem stating that every finite simple group belongs to one of four broad classes described below.

## Coding theory

Coding theory is the study of the properties of codes and their respective fitness for specific applications.

## Combination

In mathematics, a combination is a selection of items from a collection, such that (unlike permutations) the order of selection does not matter.

## Combinatorial biology

In biotechnology, combinatorial biology is the creation of a large number of compounds (usually proteins or peptides) through technologies such as phage display.

## Combinatorial chemistry

Combinatorial chemistry comprises chemical synthetic methods that make it possible to prepare a large number (tens to thousands or even millions) of compounds in a single process.

## Combinatorial data analysis

In statistics, combinatorial data analysis (CDA) is the study of data sets where the order in which objects are arranged is important.

## Combinatorial design

Combinatorial design theory is the part of combinatorial mathematics that deals with the existence, construction and properties of systems of finite sets whose arrangements satisfy generalized concepts of balance and/or symmetry.

## Combinatorial game theory

Combinatorial game theory (CGT) is a branch of mathematics and theoretical computer science that typically studies sequential games with perfect information.

## Combinatorial group theory

In mathematics, combinatorial group theory is the theory of free groups, and the concept of a presentation of a group by generators and relations.

## Combinatorial optimization

In applied mathematics and theoretical computer science, combinatorial optimization is a topic that consists of finding an optimal object from a finite set of objects.

## Combinatorial topology

In mathematics, combinatorial topology was an older name for algebraic topology, dating from the time when topological invariants of spaces (for example the Betti numbers) were regarded as derived from combinatorial decompositions of spaces, such as decomposition into simplicial complexes.

## Combinatorics and dynamical systems

The mathematical disciplines of combinatorics and dynamical systems interact in a number of ways.

## Combinatorics and physics

Combinatorial physics or physical combinatorics is the area of interaction between physics and combinatorics.

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## Complex analysis

Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.

## Computational complexity theory

Computational complexity theory is a branch of the theory of computation in theoretical computer science that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other.

## Computational geometry

Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry.

## Computer science

Computer science deals with the theoretical foundations of information and computation, together with practical techniques for the implementation and application of these foundations.

## Convex geometry

In mathematics, convex geometry is the branch of geometry studying convex sets, mainly in Euclidean space.

## Convex polytope

A convex polytope is a special case of a polytope, having the additional property that it is also a convex set of points in the n-dimensional space Rn.

## Countable set

In mathematics, a countable set is a set with the same cardinality (number of elements) as some subset of the set of natural numbers.

## Culture of Europe

The culture of Europe is rooted in the art, architecture, music, literature, and philosophy that originated from the continent of Europe.

## Decision tree

A decision tree is a decision support tool that uses a tree-like graph or model of decisions and their possible consequences, including chance event outcomes, resource costs, and utility.

## Discrete geometry

Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects.

## Discrete mathematics

Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous.

## Discrete Morse theory

Discrete Morse theory is a combinatorial adaptation of Morse theory developed by.

## Dynamical system

In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in a geometrical space.

## Encyclopædia Britannica Eleventh Edition

The Encyclopædia Britannica Eleventh Edition (1910–11) is a 29-volume reference work, an edition of the Encyclopædia Britannica.

## England in the Middle Ages

England in the Middle Ages concerns the history of England during the medieval period, from the end of the 5th century through to the start of the Early Modern period in 1485.

## Enumerative combinatorics

Enumerative combinatorics is an area of combinatorics that deals with the number of ways that certain patterns can be formed.

## Ergodic theory

Ergodic theory (Greek: έργον ergon "work", όδος hodos "way") is a branch of mathematics that studies dynamical systems with an invariant measure and related problems.

## Error correction code

In computing, telecommunication, information theory, and coding theory, an error correction code, sometimes error correcting code, (ECC) is used for controlling errors in data over unreliable or noisy communication channels.

## Eventually (mathematics)

In the mathematical areas of number theory and analysis, an infinite sequence (a_n) is said to eventually have a certain property if all terms beyond some (finite) point in the sequence have that property.

## Evolutionary biology

Evolutionary biology is the subfield of biology that studies the evolutionary processes that produced the diversity of life on Earth, starting from a single common ancestor.

## Fair division

Fair division is the problem of dividing a set of goods or resources between several people who have an entitlement to them, such that each person receives his/her due share.

## Family of sets

In set theory and related branches of mathematics, a collection F of subsets of a given set S is called a family of subsets of S, or a family of sets over S. More generally, a collection of any sets whatsoever is called a family of sets.

## Fibonacci number

In mathematics, the Fibonacci numbers are the numbers in the following integer sequence, called the Fibonacci sequence, and characterized by the fact that every number after the first two is the sum of the two preceding ones: Often, especially in modern usage, the sequence is extended by one more initial term: By definition, the first two numbers in the Fibonacci sequence are either 1 and 1, or 0 and 1, depending on the chosen starting point of the sequence, and each subsequent number is the sum of the previous two.

## Finite set

In mathematics, a finite set is a set that has a finite number of elements.

## Formal grammar

In formal language theory, a grammar (when the context is not given, often called a formal grammar for clarity) is a set of production rules for strings in a formal language.

## Formal language

In mathematics, computer science, and linguistics, a formal language is a set of strings of symbols together with a set of rules that are specific to it.

## Four color theorem

In mathematics, the four color theorem, or the four color map theorem, states that, given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colors are required to color the regions of the map so that no two adjacent regions have the same color.

## Fractal analysis

Fractal analysis is assessing fractal characteristics of data.

## Functional analysis

Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined on these spaces and respecting these structures in a suitable sense.

## 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.

## Geometric probability

Problems of the following type, and their solution techniques, were first studied in the 18th century, and the general topic became known as geometric probability.

## Geometry

Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

## Gersonides

Levi ben Gershon (1288–1344), better known by his Graecized name as Gersonides or by his Latinized name Magister Leo Hebraeus the abbreviation of first letters as RaLBaG, was a medieval French Jewish philosopher, Talmudist, mathematician, physician and astronomer/astrologer.

## Gian-Carlo Rota

Gian-Carlo Rota (April 27, 1932 &ndash; April 18, 1999) was an Italian-born American mathematician and philosopher.

## 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.

## Graph dynamical system

In mathematics, the concept of graph dynamical systems can be used to capture a wide range of processes taking place on graphs or networks.

## Graph theory

In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.

## Group theory

In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.

## H. J. Ryser

Herbert John Ryser (July 28, 1923 &ndash; July 12, 1985) was a professor of mathematics, widely regarded as one of the major figures in combinatorics in the 20th century.

## Hamiltonian path

In the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once.

## Harmonic analysis

Harmonic analysis is a branch of mathematics concerned with the representation of functions or signals as the superposition of basic waves, and the study of and generalization of the notions of Fourier series and Fourier transforms (i.e. an extended form of Fourier analysis).

## Hassler Whitney

Hassler Whitney (March 23, 1907 – May 10, 1989) was an American mathematician.

## Hipparchus

Hipparchus of Nicaea (Ἵππαρχος, Hipparkhos) was a Greek astronomer, geographer, and mathematician.

## Historian

A historian is a person who studies and writes about the past, and is regarded as an authority on it.

## Inclusion map

In mathematics, if A is a subset of B, then the inclusion map (also inclusion function, insertion, or canonical injection) is the function \iota that sends each element, x, of A to x, treated as an element of B: A "hooked arrow" is sometimes used in place of the function arrow above to denote an inclusion map; thus: \iota: A\hookrightarrow B. (On the other hand, this notation is sometimes reserved for embeddings.) This and other analogous injective functions from substructures are sometimes called natural injections.

## India

India (IAST), also called the Republic of India (IAST), is a country in South Asia.

## Information theory

Information theory studies the quantification, storage, and communication of information.

## Intersection (set theory)

In mathematics, the intersection A ∩ B of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements.

## Isaac Newton

Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, astronomer, theologian, author and physicist (described in his own day as a "natural philosopher") who is widely recognised as one of the most influential scientists of all time, and a key figure in the scientific revolution.

## Ising model

The Ising model, named after the physicist Ernst Ising, is a mathematical model of ferromagnetism in statistical mechanics.

## Jacob Bernoulli

Jacob Bernoulli (also known as James or Jacques; – 16 August 1705) was one of the many prominent mathematicians in the Bernoulli family.

## James Joseph Sylvester

James Joseph Sylvester FRS (3 September 1814 – 15 March 1897) was an English mathematician.

## Kirkman's schoolgirl problem

Kirkman's schoolgirl problem is a problem in combinatorics proposed by Rev.

## Kissing number problem

In geometry, a kissing number is defined as the number of non-overlapping unit spheres that can be arranged such that they each touch another given unit sphere.

## Lattice (order)

A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra.

## Lattice graph

A lattice graph, mesh graph, or grid graph, is a graph whose drawing, embedded in some Euclidean space Rn, forms a regular tiling.

## Leon Mirsky

Leonid Mirsky (19 December 1918 Russia – 1 December 1983 Sheffield, England) was a Russian-British mathematician who worked in number theory, linear algebra, and combinatorics.

## 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.

## Linear independence

In the theory of vector spaces, a set of vectors is said to be if one of the vectors in the set can be defined as a linear combination of the others; if no vector in the set can be written in this way, then the vectors are said to be.

## Linguistics

Linguistics is the scientific study of language, and involves an analysis of language form, language meaning, and language in context.

## Logic

Logic (from the logikḗ), originally meaning "the word" or "what is spoken", but coming to mean "thought" or "reason", is a subject concerned with the most general laws of truth, and is now generally held to consist of the systematic study of the form of valid inference.

## Mahāvīra (mathematician)

Mahāvīra (or Mahaviracharya, "Mahavira the Teacher") was a 9th-century Jain mathematician from Karnataka, India.

## Markov chain

A Markov chain is "a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event".

## Markov chain mixing time

In probability theory, the mixing time of a Markov chain is the time until the Markov chain is "close" to its steady state distribution.

## Mathematical logic

Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics.

## Mathematical problem

A mathematical problem is a problem that is amenable to being represented, analyzed, and possibly solved, with the methods of mathematics.

## Mathematical structure

In mathematics, a structure on a set is an additional mathematical object that, in some manner, attaches (or relates) to that set to endow it with some additional meaning or significance.

## Mathematician

A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.

## Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

## MathWorld

MathWorld is an online mathematics reference work, created and largely written by Eric W. Weisstein.

## Metric space

In mathematics, a metric space is a set for which distances between all members of the set are defined.

## Middle Ages

In the history of Europe, the Middle Ages (or Medieval Period) lasted from the 5th to the 15th century.

## Necklace problem

The necklace problem is a problem in recreational mathematics, solved in the early 21st century.

## Number theory

Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.

## Operations research

Operations research, or operational research in British usage, is a discipline that deals with the application of advanced analytical methods to help make better decisions.

## 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.

## Ostomachion

Ostomachion, also known as loculus Archimedius (Archimedes' box in Latin) and also as syntomachion, is a mathematical treatise attributed to Archimedes.

## Outline of combinatorics

Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures.

## Partially ordered set

In mathematics, especially order theory, a partially ordered set (also poset) formalizes and generalizes the intuitive concept of an ordering, sequencing, or arrangement of the elements of a set.

## Partition (number theory)

In number theory and combinatorics, a partition of a positive integer n, also called an integer partition, is a way of writing n as a sum of positive integers.

## Partition of a set

In mathematics, a partition of a set is a grouping of the set's elements into non-empty subsets, in such a way that every element is included in one and only one of the subsets.

## Pascal's triangle

In mathematics, Pascal's triangle is a triangular array of the binomial coefficients.

## Paul Erdős

Paul Erdős (Erdős Pál; 26 March 1913 – 20 September 1996) was a Hungarian mathematician.

## Percy Alexander MacMahon

Percy Alexander MacMahon (born 26 September 1854, Sliema, British Malta &ndash; 25 December 1929, Bognor Regis, England) was a mathematician, especially noted in connection with the partitions of numbers and enumerative combinatorics.

## 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.

## Permutohedron

In mathematics, the permutohedron of order n (also spelled permutahedron) is an (n &minus; 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).

## Philosopher

A philosopher is someone who practices philosophy, which involves rational inquiry into areas that are outside either theology or science.

## Phylogenetics

In biology, phylogenetics (Greek: φυλή, φῦλον – phylé, phylon.

## Physician

A physician, medical practitioner, medical doctor, or simply doctor is a professional who practises medicine, which is concerned with promoting, maintaining, or restoring health through the study, diagnosis, and treatment of disease, injury, and other physical and mental impairments.

## Pigeonhole principle

In mathematics, the pigeonhole principle states that if items are put into containers, with, then at least one container must contain more than one item.

## Plutarch

Plutarch (Πλούταρχος, Ploútarkhos,; c. CE 46 – CE 120), later named, upon becoming a Roman citizen, Lucius Mestrius Plutarchus, (Λούκιος Μέστριος Πλούταρχος) was a Greek biographer and essayist, known primarily for his Parallel Lives and Moralia.

## Polyhedral combinatorics

Polyhedral combinatorics is a branch of mathematics, within combinatorics and discrete geometry, that studies the problems of counting and describing the faces of convex polyhedra and higher-dimensional convex polytopes.

## Potts model

In statistical mechanics, the Potts model, a generalization of the Ising model, is a model of interacting spins on a crystalline lattice.

## Power set

In mathematics, the power set (or powerset) of any set is the set of all subsets of, including the empty set and itself, variously denoted as, 𝒫(), ℘() (using the "Weierstrass p"),,, or, identifying the powerset of with the set of all functions from to a given set of two elements,.

## Probabilistic method

The probabilistic method is a nonconstructive method, primarily used in combinatorics and pioneered by Paul Erdős, for proving the existence of a prescribed kind of mathematical object.

## Probabilistic number theory

Probabilistic number theory is a subfield of number theory, which explicitly uses probability to answer questions of number theory.

## Probability

Probability is the measure of the likelihood that an event will occur.

## Probability theory

Probability theory is the branch of mathematics concerned with probability.

## Pure mathematics

Broadly speaking, pure mathematics is mathematics that studies entirely abstract concepts.

## 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.

## Ramsey theory

Ramsey theory, named after the British mathematician and philosopher Frank P. Ramsey, is a branch of mathematics that studies the conditions under which order must appear.

## Random graph

In mathematics, random graph is the general term to refer to probability distributions over graphs.

## Real projective space

In mathematics, real projective space, or RPn or \mathbb_n(\mathbb), is the topological space of lines passing through the origin 0 in Rn+1.

## Renaissance

The Renaissance is a period in European history, covering the span between the 14th and 17th centuries.

## 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.

## 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.

## 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.

## Science

R. P. Feynman, The Feynman Lectures on Physics, Vol.1, Chaps.1,2,&3.

## Set theory

Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.

## Special functions

Special functions are particular mathematical functions which have more or less established names and notations due to their importance in mathematical analysis, functional analysis, physics, or other applications.

## Statistical mechanics

Statistical mechanics is one of the pillars of modern physics.

## Statistical physics

Statistical physics is a branch of physics that uses methods of probability theory and statistics, and particularly the mathematical tools for dealing with large populations and approximations, in solving physical problems.

## Steiner system

The Fano plane is an S(2,3,7) Steiner triple system. The blocks are the 7 lines, each containing 3 points. Every pair of points belongs to a unique line. In combinatorial mathematics, a Steiner system (named after Jakob Steiner) is a type of block design, specifically a t-design with λ.

## Sushruta

Sushruta, or Suśruta (Sanskrit: सुश्रुत, lit. "well heard") was an ancient Indian physician during 1500 BCE to 1000 BCE, known as the main author of the treatise The Compendium of Suśruta (Sanskrit: ''Suśruta-saṃhitā'').

## Sushruta Samhita

The Sushruta Samhita (सुश्रुतसंहिता, IAST: Suśrutasaṃhitā, literally "Suśruta's Compendium") is an ancient Sanskrit text on medicine and surgery, and one of the most important such treatises on this subject to survive from the ancient world.

## Symbolic method (combinatorics)

In combinatorics, especially in analytic combinatorics, the symbolic method is a technique for counting combinatorial objects.

## Talmud

The Talmud (Hebrew: תַּלְמוּד talmūd "instruction, learning", from a root LMD "teach, study") is the central text of Rabbinic Judaism and the primary source of Jewish religious law and theology.

## Theoretical computer science

Theoretical computer science, or TCS, is a subset of general computer science and mathematics that focuses on more mathematical topics of computing and includes the theory of computation.

## Tiling puzzle

Tiling puzzles are puzzles involving two-dimensional packing problems in which a number of flat shapes have to be assembled into a larger given shape without overlaps (and often without gaps).

## Timeline of Indian history

This is a timeline of Indian history, comprising important legal and territorial changes and political events in India and its predecessor states.

## Topology

In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, crumpling and bending, but not tearing or gluing.

## Triangle-free graph

In the mathematical area of graph theory, a triangle-free graph is an undirected graph in which no three vertices form a triangle of edges.

## Tutte polynomial

The Tutte polynomial, also called the dichromate or the Tutte–Whitney polynomial, is a graph polynomial.

## 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.

## Two-dimensional space

Two-dimensional space or bi-dimensional space is a geometric setting in which two values (called parameters) are required to determine the position of an element (i.e., point).

## Vector space

A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.

## Vertex (graph theory)

In mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph consists of a set of vertices and a set of arcs (ordered pairs of vertices).

## References

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