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. It is closely related to many other areas of mathematics and has many a ...

is a branch of mathematics concerning the study of finite or

countable In mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers. Equivalently, a set is ''countable'' if there exists an injective function from it into the natural number ...

discrete Discrete may refer to: *Discrete particle or quantum in physics, for example in quantum theory *Discrete device, an electronic component with just one circuit element, either passive or active, other than an integrated circuit *Discrete group, a ...

structures.

Essence of combinatorics

Matroid In combinatorics, a branch of mathematics, a matroid is a structure that abstracts and generalizes the notion of linear independence in vector spaces. There are many equivalent ways to define a matroid axiomatically, the most significant being ...

* Greedoid *

Ramsey theory Ramsey theory, named after the British mathematician and philosopher Frank P. Ramsey, is a branch of mathematics that focuses on the appearance of order in a substructure given a structure of a known size. Problems in Ramsey theory typically ask ...

Van der Waerden's theorem Van der Waerden's theorem is a theorem in the branch of mathematics called Ramsey theory. Van der Waerden's theorem states that for any given positive integers ''r'' and ''k'', there is some number ''N'' such that if the integers are colored, ea ...

Hales–Jewett theorem In mathematics, the Hales–Jewett theorem is a fundamental combinatorial result of Ramsey theory named after Alfred W. Hales and Robert I. Jewett, concerning the degree to which high-dimensional objects must necessarily exhibit some combinatori ...

Umbral calculus In mathematics before the 1970s, the term umbral calculus referred to the surprising similarity between seemingly unrelated polynomial equations and certain "shadowy" techniques used to "prove" them. These techniques were introduced by John Bliss ...

binomial type In mathematics, a polynomial sequence, i.e., a sequence of polynomials indexed by non-negative integers \left\ in which the index of each polynomial equals its degree, is said to be of binomial type if it satisfies the sequence of identities :p ...

polynomial sequences *

Combinatorial species In combinatorial mathematics, the theory of combinatorial species is an abstract, systematic method for deriving the generating functions of discrete structures, which allows one to not merely count these structures but give bijective proofs in ...

Branches of combinatorics

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 alg ...

Analytic combinatorics In combinatorics, the symbolic method is a technique for counting combinatorial objects. It uses the internal structure of the objects to derive formulas for their generating functions. The method is mostly associated with Philippe Flajolet an ...

Arithmetic combinatorics In mathematics, arithmetic combinatorics is a field in the intersection of number theory, combinatorics, ergodic theory and harmonic analysis. Scope Arithmetic combinatorics is about combinatorial estimates associated with arithmetic operations (a ...

Combinatorics on words Combinatorics on words is a fairly new field of mathematics, branching from combinatorics, which focuses on the study of words and formal languages. The subject looks at letters or symbols, and the sequences they form. Combinatorics on words a ...

Combinatorial design theory 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''. These c ...

Enumerative combinatorics Enumerative combinatorics is an area of combinatorics that deals with the number of ways that certain patterns can be formed. Two examples of this type of problem are counting combinations and counting permutations. More generally, given an infin ...

* Extremal combinatorics * Geometric combinatorics *

Graph theory In mathematics, graph theory is the study of '' graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conn ...

Infinitary combinatorics In mathematics, infinitary combinatorics, or combinatorial set theory, is an extension of ideas in combinatorics to infinite sets. Some of the things studied include continuous graphs and trees, extensions of Ramsey's theorem, and Martin's axiom. ...

Matroid theory In combinatorics, a branch of mathematics, a matroid is a structure that abstracts and generalizes the notion of linear independence in vector spaces. There are many equivalent ways to define a matroid axiomatically, the most significant being ...

Order theory Order theory is a branch of mathematics that investigates the intuitive notion of order using binary relations. It provides a formal framework for describing statements such as "this is less than that" or "this precedes that". This article intr ...

Partition theory In number theory and combinatorics, a partition of a positive integer , also called an integer partition, is a way of writing as a sum of positive integers. Two sums that differ only in the order of their summands are considered the same part ...

Probabilistic combinatorics 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. It works by showing that if one randomly chooses objects fro ...

Topological combinatorics The mathematical discipline of topological combinatorics is the application of topological and algebro-topological methods to solving problems in combinatorics. History The discipline of combinatorial topology used combinatorial concepts in to ...

Multi-disciplinary fields that include combinatorics

Coding theory Coding theory is the study of the properties of codes and their respective fitness for specific applications. Codes are used for data compression, cryptography, error detection and correction, data transmission and data storage. Codes are stud ...

Combinatorial optimization Combinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, where the set of feasible solutions is discrete or can be reduced to a discrete set. Typical combi ...

* Combinatorics and dynamical systems * Combinatorics and physics *

Discrete geometry Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric objects. Most questions in discrete geometry involve finite or discrete sets of basic ge ...

Finite geometry Finite is the opposite of infinite. It may refer to: * Finite number (disambiguation) * Finite set, a set whose cardinality (number of elements) is some natural number * Finite verb Traditionally, a finite verb (from la, fīnītus, past particip ...

Phylogenetics In biology, phylogenetics (; from Greek φυλή/ φῦλον [] "tribe, clan, race", and wikt:γενετικός, γενετικός [] "origin, source, birth") is the study of the evolutionary history and relationships among or within groups ...

History of combinatorics

History of combinatorics The mathematical field of combinatorics was studied to varying degrees in numerous ancient societies. Its study in Europe dates to the work of Leonardo Fibonacci in the 13th century AD, which introduced Arabian and Indian ideas to the continent. ...

General combinatorial principles and methods

Combinatorial principles In proving results in combinatorics several useful combinatorial rules or combinatorial principles are commonly recognized and used. The rule of sum, rule of product, and inclusion–exclusion principle are often used for enumerative purposes. Bi ...

Trial and error Trial and error is a fundamental method of problem-solving characterized by repeated, varied attempts which are continued until success, or until the practicer stops trying. According to W.H. Thorpe, the term was devised by C. Lloyd Morgan ( ...

brute-force search In computer science, brute-force search or exhaustive search, also known as generate and test, is a very general problem-solving technique and algorithmic paradigm that consists of systematically enumerating all possible candidates for the soluti ...

bogosort In computer science, bogosort (also known as permutation sort, stupid sort, slowsort or bozosort) is a sorting algorithm based on the generate and test paradigm. The function successively generates permutations of its input until it finds one t ...

British Museum algorithm The British Museum algorithm is a general approach to finding a solution by checking all possibilities one by one, beginning with the smallest. The term refers to a conceptual, not a practical, technique where the number of possibilities is enor ...

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. For example, if one has three gloves (and none is ambidextrous/reversible), then there m ...

Method of distinguished element In the mathematical field of enumerative combinatorics, identities are sometimes established by arguments that rely on singling out one "distinguished element" of a set. Definition Let \mathcal be a family of subsets of the set A and let x \in ...

Mathematical induction Mathematical induction is a method for proving that a statement ''P''(''n'') is true for every natural number ''n'', that is, that the infinitely many cases ''P''(0), ''P''(1), ''P''(2), ''P''(3), ... all hold. Informal metaphors help ...

Recurrence relation In mathematics, a recurrence relation is an equation according to which the nth term of a sequence of numbers is equal to some combination of the previous terms. Often, only k previous terms of the sequence appear in the equation, for a paramete ...

telescoping series In mathematics, a telescoping series is a series whose general term t_n can be written as t_n=a_n-a_, i.e. the difference of two consecutive terms of a sequence (a_n). As a consequence the partial sums only consists of two terms of (a_n) after ...

Generating function In mathematics, a generating function is a way of encoding an infinite sequence of numbers () by treating them as the coefficients of a formal power series. This series is called the generating function of the sequence. Unlike an ordinary ser ...

s as an application of

formal power series In mathematics, a formal series is an infinite sum that is considered independently from any notion of convergence, and can be manipulated with the usual algebraic operations on series (addition, subtraction, multiplication, division, partial s ...

** Cyclic sieving **

Schrödinger method In combinatorial mathematics and probability theory, the Schrödinger method, named after the Austrian physicist Erwin Schrödinger, is used to solve some problems of distribution and occupancy. Suppose :X_1,\dots,X_n \, are independent random ...

Exponential generating function In mathematics, a generating function is a way of encoding an infinite sequence of numbers () by treating them as the coefficients of a formal power series. This series is called the generating function of the sequence. Unlike an ordinary ser ...

Stanley's reciprocity theorem In combinatorial mathematics, Stanley's reciprocity theorem, named after MIT mathematician Richard P. Stanley, states that a certain functional equation is satisfied by the generating function of any rational cone (defined below) and the generati ...

Binomial coefficient In mathematics, the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem. Commonly, a binomial coefficient is indexed by a pair of integers and is written \tbinom. It is the coefficient of the t ...

s and their properties *

Combinatorial proof In mathematics, the term ''combinatorial proof'' is often used to mean either of two types of mathematical proof: * A proof by double counting. A combinatorial identity is proven by counting the number of elements of some carefully chosen set ...

Double counting (proof technique) In combinatorics, double counting, also called counting in two ways, is a combinatorial proof technique for showing that two expressions are equal by demonstrating that they are two ways of counting the size of one set. In this technique, which ...

Bijective proof In combinatorics, bijective proof is a proof technique for proving that two sets have equally many elements, or that the sets in two combinatorial classes have equal size, by finding a bijective function that maps one set one-to-one onto the othe ...

Inclusion–exclusion principle In combinatorics, a branch of 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 : , A \c ...

Möbius inversion formula In mathematics, the classic Möbius inversion formula is a relation between pairs of arithmetic functions, each defined from the other by sums over divisors. It was introduced into number theory in 1832 by August Ferdinand Möbius. A large genera ...

* Parity,

even and odd permutations In mathematics, when ''X'' is a finite set with 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. If any total ...

Combinatorial Nullstellensatz In additive number theory and combinatorics, a restricted sumset has the form :S=\, where A_1,\ldots,A_n are finite nonempty subsets of a field ''F'' and P(x_1,\ldots,x_n) is a polynomial over ''F''. If P is a constant non-zero function, for ...

Incidence algebra In order theory, a field of mathematics, an incidence algebra is an associative algebra, defined for every locally finite partially ordered set and commutative ring with unity. Subalgebras called reduced incidence algebras give a natural construct ...

Greedy algorithm A greedy algorithm is any algorithm that follows the problem-solving heuristic of making the locally optimal choice at each stage. In many problems, a greedy strategy does not produce an optimal solution, but a greedy heuristic can yield locall ...

Divide and conquer algorithm In computer science Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to practical ...

** Akra–Bazzi method *

Dynamic programming Dynamic programming is both a mathematical optimization method and a computer programming method. The method was developed by Richard Bellman in the 1950s and has found applications in numerous fields, from aerospace engineering to economics. I ...

Branch and bound Branch and bound (BB, B&B, or BnB) is an algorithm design paradigm for discrete and combinatorial optimization problems, as well as mathematical optimization. A branch-and-bound algorithm consists of a systematic enumeration of candidate solutio ...

* Birthday attack,

birthday paradox In probability theory, the birthday problem asks for the probability that, in a set of randomly chosen people, at least two will share a birthday. The birthday paradox is that, counterintuitively, the probability of a shared birthday exceeds 5 ...

Floyd's cycle-finding algorithm In computer science, cycle detection or cycle finding is the algorithmic problem of finding a cycle in a sequence of iterated function values. For any function (mathematics), function that maps a finite set to itself, and any initial value in ...

* Reduction to

linear algebra Linear algebra is the branch of mathematics concerning linear equations such as: :a_1x_1+\cdots +a_nx_n=b, linear maps such as: :(x_1, \ldots, x_n) \mapsto a_1x_1+\cdots +a_nx_n, and their representations in vector spaces and through matric ...

Sparsity In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. There is no strict definition regarding the proportion of zero-value elements for a matrix to qualify as sparse b ...

Weight function A weight function is a mathematical device used when performing a sum, integral, or average to give some elements more "weight" or influence on the result than other elements in the same set. The result of this application of a weight function is ...

Minimax algorithm Minimax (sometimes MinMax, MM or saddle point) is a decision rule used in artificial intelligence, decision theory, game theory, statistics, and philosophy for ''mini''mizing the possible loss for a worst case (''max''imum loss) scenario. Whe ...

Alpha–beta pruning Alpha–beta pruning is a search algorithm that seeks to decrease the number of nodes that are evaluated by the minimax algorithm in its search tree. It is an adversarial search algorithm used commonly for machine playing of two-player games ...

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. It works by showing that if one randomly chooses objects fr ...

* Sieve methods *

Symbolic combinatorics In combinatorics, the symbolic method is a technique for enumerative combinatorics, counting combinatorial objects. It uses the internal structure of the objects to derive formulas for their generating functions. The method is mostly associated ...

Combinatorial class In mathematics, a combinatorial class is a countable set of mathematical objects, together with a size function mapping each object to a non-negative integer, such that there are finitely many objects of each size. Counting sequences and isomorphi ...

Exponential formula In combinatorial mathematics, the exponential formula (called the polymer expansion in physics) states that the exponential generating function for structures on finite sets is the exponential of the exponential generating function for connected s ...

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 ...

MacMahon Master theorem In mathematics, MacMahon's master theorem (MMT) is a result in enumerative combinatorics and linear algebra. It was discovered by Percy MacMahon and proved in his monograph ''Combinatory analysis'' (1916). It is often used to derive binomial iden ...

Data structure concepts

Data structure In computer science, a data structure is a data organization, management, and storage format that is usually chosen for Efficiency, efficient Data access, access to data. More precisely, a data structure is a collection of data values, the rel ...

Data type In computer science and computer programming, a data type (or simply type) is a set of possible values and a set of allowed operations on it. A data type tells the compiler or interpreter how the programmer intends to use the data. Most progra ...

Abstract data type In computer science, an abstract data type (ADT) is a mathematical model for data types. An abstract data type is defined by its behavior (semantics) from the point of view of a '' user'', of the data, specifically in terms of possible values, po ...

Algebraic data type In computer programming, especially functional programming and type theory, an algebraic data type (ADT) is a kind of composite type, i.e., a type formed by combining other types. Two common classes of algebraic types are product types (i.e., ...

Composite type In computer science, a composite data type or compound data type is any data type which can be constructed in a program using the programming language's primitive data types and other composite types. It is sometimes called a structure or aggreg ...

Array An array is a systematic arrangement of similar objects, usually in rows and columns. Things called an array include: {{TOC right Music * In twelve-tone and serial composition, the presentation of simultaneous twelve-tone sets such that the ...

Associative array In computer science, an associative array, map, symbol table, or dictionary is an abstract data type that stores a collection of (key, value) pairs, such that each possible key appears at most once in the collection. In mathematical terms an ...

Deque In computer science, a double-ended queue (abbreviated to deque, pronounced ''deck'', like "cheque") is an abstract data type that generalizes a queue, for which elements can be added to or removed from either the front (head) or back (tail). I ...

List A ''list'' is any set of items in a row. List or lists may also refer to: People * List (surname) Organizations * List College, an undergraduate division of the Jewish Theological Seminary of America * SC Germania List, German rugby uni ...

Linked list In computer science, a linked list is a linear collection of data elements whose order is not given by their physical placement in memory. Instead, each element points to the next. It is a data structure consisting of a collection of nodes whi ...

Queue __NOTOC__ Queue () may refer to: * Queue area, or queue, a line or area where people wait for goods or services Arts, entertainment, and media *''ACM Queue'', a computer magazine * ''The Queue'' (Sorokin novel), a 1983 novel by Russian author ...

Priority queue In computer science, a priority queue is an abstract data-type similar to a regular queue or stack data structure in which each element additionally has a ''priority'' associated with it. In a priority queue, an element with high priority is se ...

Skip list In computer science, a skip list (or skiplist) is a probabilistic data structure that allows \mathcal(\log n) average complexity for search as well as \mathcal(\log n) average complexity for insertion within an ordered sequence of n elements. ...

Stack Stack may refer to: Places * Stack Island, an island game reserve in Bass Strait, south-eastern Australia, in Tasmania’s Hunter Island Group * Blue Stack Mountains, in Co. Donegal, Ireland People * Stack (surname) (including a list of people ...

Tree data structure In computer science, a tree is a widely used abstract data type that represents a hierarchical tree structure with a set of connected nodes. Each node in the tree can be connected to many children (depending on the type of tree), but must be con ...

Automatic garbage collection In computer science, garbage collection (GC) is a form of automatic memory management. The ''garbage collector'' attempts to reclaim memory which was allocated by the program, but is no longer referenced; such memory is called ''garbage''. G ...

Problem solving as an art

Heuristic A heuristic (; ), or heuristic technique, is any approach to problem solving or self-discovery that employs a practical method that is not guaranteed to be optimal, perfect, or rational, but is nevertheless sufficient for reaching an immediat ...

* Inductive reasoning * ''

How to Solve It ''How to Solve It'' (1945) is a small volume by mathematician George Pólya describing methods of problem solving. Four principles ''How to Solve It'' suggests the following steps when solving a mathematical problem: # First, you have to ''und ...

'' *

Creative problem solving Creative problem-solving (CPS) is the mental process of searching for an original and previously unknown solution to a problem. To qualify, the solution must be novel and reached independently. The creative problem-solving process was originally de ...

Morphological analysis (problem-solving) Morphological analysis is the analysis of morphology in various fields * Morphological analysis (problem-solving) or general morphological analysis, a method for exploring all possible solutions to a multi-dimensional, non-quantified problem * An ...

Living with large numbers

Names of large numbers Two naming scales for large numbers have been used in English and other European languages since the early modern era: the long and short scales. Most English variants use the short scale today, but the long scale remains dominant in many non-En ...

long scale The long and short scales are two of several naming systems for integer powers of ten which use some of the same terms for different magnitudes. For whole numbers smaller than 1,000,000,000 (109), such as one thousand or one million, the t ...

History of large numbers Different cultures used different traditional numeral systems for naming large numbers. The extent of large numbers used varied in each culture. Two interesting points in using large numbers are the confusion on the term billion and milliard in man ...

Graham's number Graham's number is an immense number that arose as an upper bound on the answer of a problem in the mathematical field of Ramsey theory. It is much larger than many other large numbers such as Skewes's number and Moser's number, both of which ar ...

* Moser's number *

Skewes' number In number theory, Skewes's number is any of several large numbers used by the South African mathematician Stanley Skewes as upper bounds for the smallest natural number x for which :\pi(x) > \operatorname(x), where is the prime-counting function ...

* ''Large number notations'' **

Conway chained arrow notation Conway chained arrow notation, created by mathematician John Horton Conway, is a means of expressing certain extremely large numbers. It is simply a finite sequence of positive integers separated by rightward arrows, e.g. 2\to3\to4\to5\to6. As wit ...

** Hyper4 **

Knuth's up-arrow notation In mathematics, Knuth's up-arrow notation is a method of notation for very large integers, introduced by Donald Knuth in 1976. In his 1947 paper, R. L. Goodstein introduced the specific sequence of operations that are now called ''hyperoperat ...

** Moser polygon notation **

Steinhaus polygon notation Steinhaus may refer to: * Bibiana Steinhaus, German football referee * Edward Arthur Steinhaus (1914–1969), American insect pathologist * Hugo Steinhaus, mathematician * Steinhaus, Austria, a municipality in Upper Austria, Austria * Steinhaus, Sw ...

* ''Large number effects'' **

Exponential growth Exponential growth is a process that increases quantity over time. It occurs when the instantaneous rate of change (that is, the derivative) of a quantity with respect to time is proportional to the quantity itself. Described as a function, a ...

Combinatorial explosion In mathematics, a combinatorial explosion is the rapid growth of the complexity of a problem due to how the combinatorics of the problem is affected by the input, constraints, and bounds of the problem. Combinatorial explosion is sometimes used to ...

Branching factor In computing, tree data structures, and game theory, the branching factor is the number of children at each node, the outdegree. If this value is not uniform, an ''average branching factor'' can be calculated. For example, in chess, if a "node" ...

Granularity Granularity (also called graininess), the condition of existing in granules or grains, refers to the extent to which a material or system is composed of distinguishable pieces. It can either refer to the extent to which a larger entity is su ...

Curse of dimensionality The curse of dimensionality refers to various phenomena that arise when analyzing and organizing data in high-dimensional spaces that do not occur in low-dimensional settings such as the three-dimensional physical space of everyday experience. Th ...

Concentration of measure In mathematics, concentration of measure (about a median) is a principle that is applied in measure theory, probability and combinatorics, and has consequences for other fields such as Banach space theory. Informally, it states that "A random ...

Persons influential in the field of combinatorics

Noga Alon Noga Alon ( he, נוגה אלון; born 17 February 1956) is an Israeli mathematician and a professor of mathematics at Princeton University noted for his contributions to combinatorics and theoretical computer science, having authored hundreds of ...

* George Andrews * József Beck *

Eric Temple Bell Eric Temple Bell (7 February 1883 – 21 December 1960) was a Scottish-born mathematician and science fiction writer who lived in the United States for most of his life. He published non-fiction using his given name and fiction as John Tai ...

Claude Berge Claude Jacques Berge (5 June 1926 – 30 June 2002) was a French mathematician, recognized as one of the modern founders of combinatorics and graph theory. Biography and professional history Claude Berge's parents were André Berge and Geneviève ...

Béla Bollobás Béla Bollobás FRS (born 3 August 1943) is a Hungarian-born British mathematician who has worked in various areas of mathematics, including functional analysis, combinatorics, graph theory, and percolation. He was strongly influenced by Paul ...

* Peter Cameron * Louis Comtet *

John Horton Conway John Horton Conway (26 December 1937 – 11 April 2020) was an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He also made contributions to many branc ...

On Numbers and Games ''On Numbers and Games'' is a mathematics book by John Horton Conway first published in 1976. The book is written by a pre-eminent mathematician, and is directed at other mathematicians. The material is, however, developed in a playful and unpr ...

** Winning Ways for your Mathematical Plays *

Persi Diaconis Persi Warren Diaconis (; born January 31, 1945) is an American mathematician of Greek descent and former professional magician. He is the Mary V. Sunseri Professor of Statistics and Mathematics at Stanford University. He is particularly know ...

* Ada Dietz * Paul Erdős **

Erdős conjecture Erdős, Erdos, or Erdoes is a Hungarian surname. People with the surname include: * Ágnes Erdős (born 1950), Hungarian politician * Brad Erdos (born 1990), Canadian football player * Éva Erdős (born 1964), Hungarian handball player * Józ ...

* Philippe Flajolet *

Solomon Golomb Solomon (; , ),, ; ar, سُلَيْمَان, ', , ; el, Σολομών, ; la, Salomon also called Jedidiah ( Hebrew: , Modern: , Tiberian: ''Yăḏīḏăyāh'', "beloved of Yah"), was a monarch of ancient Israel and the son and succe ...

* Ron Graham * Ben Green *

Tim Gowers Sir William Timothy Gowers, (; born 20 November 1963) is a British mathematician. He is Professeur titulaire of the Combinatorics chair at the Collège de France, and director of research at the University of Cambridge and Fellow of Trinity ...

Jeff Kahn Jeffry Ned Kahn is a professor of mathematics at Rutgers University notable for his work in combinatorics. Education Kahn received his Ph.D. from Ohio State University in 1979 after completing his dissertation under his advisor Dijen K. Ray-Chau ...

Gil Kalai Gil Kalai (born 1955) is the Henry and Manya Noskwith Professor Emeritus of Mathematics at the Hebrew University of Jerusalem, Israel, Professor of Computer Science at the Interdisciplinary Center, Herzliya, and adjunct Professor of mathematics ...

Gyula O. H. Katona Gyula O. H. Katona (born 16 March 1941 in Budapest) is a Hungarian mathematician known for his work in combinatorial set theory, and especially for the Kruskal–Katona theorem and his beautiful and elegant proof of the Erdős–Ko–Rado the ...

Daniel J. Kleitman Daniel J. Kleitman (born October 4, 1934)article availableon Douglas West (mathematician), Douglas West's web page, University of Illinois at Urbana–Champaign)."Kleitman, Daniel J.," in: ''Who's Who in Frontier Science and Technology'', 1, 1984, ...

Imre Leader Imre Bennett Leader is a British Othello player, employed as a professor of pure mathematics at Cambridge University. As a child, he was a pupil at the private St Paul's School and won a silver medal on the British team at the 1981 Internati ...

László Lovász László Lovász (; born March 9, 1948) is a Hungarian mathematician and professor emeritus at Eötvös Loránd University, best known for his work in combinatorics, for which he was awarded the 2021 Abel Prize jointly with Avi Wigderson. He wa ...

Fedor Petrov Fyodor, Fedor (russian: Фёдор) or Feodor is the Russian form of the name " Theodore" meaning “God’s Gift”. Fedora () is the feminine form. Fyodor and Fedor are two English transliterations of the same Russian name. It may refer to: Gi ...

George Pólya George Pólya (; hu, Pólya György, ; December 13, 1887 – September 7, 1985) was a Hungarian mathematician. He was a professor of mathematics from 1914 to 1940 at ETH Zürich and from 1940 to 1953 at Stanford University. He made fundamenta ...

Vojtěch Rödl Vojtěch Rödl (born 1 April 1949) is a Czech American mathematician, Samuel Candler Dobbs Professor at Emory University. He is noted for his contributions mainly to combinatorics having authored hundreds of research papers. Academic Background ...

Gian-Carlo Rota Gian-Carlo Rota (April 27, 1932 – April 18, 1999) was an Italian-American mathematician and philosopher. He spent most of his career at the Massachusetts Institute of Technology, where he worked in combinatorics, functional analysis, prob ...

Cecil C. Rousseau Cecil Clyde Rousseau, Jr. (January 13, 1938 Philadelphia - April 10, 2020 Memphis) was a mathematician and author who specialized in graph theory and combinatorics. He was a professor at The University of Memphis starting in 1970 until retiri ...

* H. J. Ryser * Dick Schelp * Vera T. Sós *

Joel Spencer Joel Spencer (born April 20, 1946) is an American mathematician. He is a combinatorialist who has worked on probabilistic methods in combinatorics and on Ramsey theory. He received his doctorate from Harvard University in 1970, under the supervis ...

Emanuel Sperner Emanuel Sperner (9 December 1905 – 31 January 1980) was a German mathematician, best known for two theorems. He was born in Waltdorf (near Neiße, Upper Silesia, now Nysa, Poland), and died in Sulzburg-Laufen, West Germany. He was a student at ...

* Richard P. Stanley * Benny Sudakov *

Endre Szemerédi Endre Szemerédi (; born August 21, 1940) is a Hungarian-American mathematician and computer scientist, working in the field of combinatorics and theoretical computer science. He has been the State of New Jersey Professor of computer science a ...

Terence Tao Terence Chi-Shen Tao (; born 17 July 1975) is an Australian-American mathematician. He is a professor of mathematics at the University of California, Los Angeles (UCLA), where he holds the James and Carol Collins chair. His research includes ...

Carsten Thomassen Carsten Thomassen may refer to: * Carsten Thomassen (mathematician) * Carsten Thomassen (journalist) Carsten Thomassen (15 May 1969 – 14 January 2008) was a Norwegian journalist, political commentator and war correspondent for the Norwegi ...

* Jacques Touchard *

Pál Turán Pál Turán (; 18 August 1910 – 26 September 1976) also known as Paul Turán, was a Hungarian mathematician who worked primarily in extremal combinatorics. He had a long collaboration with fellow Hungarian mathematician Paul Erdős, lasting ...

Bartel Leendert van der Waerden Bartel Leendert van der Waerden (; 2 February 1903 – 12 January 1996) was a Dutch mathematician and historian of mathematics. Biography Education and early career Van der Waerden learned advanced mathematics at the University of Amster ...

Herbert Wilf Herbert Saul Wilf (June 13, 1931 – January 7, 2012) was a mathematician, specializing in combinatorics and graph theory. He was the Thomas A. Scott Professor of Mathematics in Combinatorial Analysis and Computing at the University of Pennsylv ...

* Richard Wilson *

Doron Zeilberger Doron Zeilberger (דורון ציילברגר, born 2 July 1950 in Haifa, Israel) is an Israeli mathematician, known for his work in combinatorics. Education and career He received his doctorate from the Weizmann Institute of Science in 1976, ...

Combinatorics scholars

* :Combinatorialists

Journals

* Advances in Combinatorics * Annals of Combinatorics * Ars Combinatoria * Australasian Journal of Combinatorics * Bulletin of the Institute of Combinatorics and Its Applications *

Combinatorica ''Combinatorica'' is an international journal of mathematics, publishing papers in the fields of combinatorics and computer science. It started in 1981, with László Babai and László Lovász as the editors-in-chief with Paul Erdős as hono ...

Combinatorics, Probability and Computing ''Combinatorics, Probability and Computing'' is a peer-reviewed scientific journal in mathematics published by Cambridge University Press. Its editor-in-chief is Béla Bollobás (DPMMS and University of Memphis). History The journal was establ ...

Computational Complexity In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given to computation time (generally measured by the number of needed elementary operations) ...

* Designs, Codes and Cryptography * Discrete Analysis *

Discrete and Computational Geometry '' Discrete & Computational Geometry'' is a peer-reviewed mathematics journal published quarterly by Springer. Founded in 1986 by Jacob E. Goodman and Richard M. Pollack, the journal publishes articles on discrete geometry and computational ge ...

* Discrete Applied Mathematics *

Discrete Mathematics Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection with the set of natural numbers) rather than "continuous" (analogously to continu ...

* Discrete Mathematics & Theoretical Computer Science * Discrete Optimization * Discussiones Mathematicae Graph Theory *

Electronic Journal of Combinatorics The ''Electronic Journal of Combinatorics'' is a peer-reviewed open access scientific journal covering research in combinatorial mathematics. The journal was established in 1994 by Herbert Wilf (University of Pennsylvania) and Neil Calkin (Georg ...

European Journal of Combinatorics European, or Europeans, or Europeneans, may refer to: In general * ''European'', an adjective referring to something of, from, or related to Europe ** Ethnic groups in Europe ** Demographics of Europe ** European cuisine European cuisine co ...

The Fibonacci Quarterly The ''Fibonacci Quarterly'' is a scientific journal on mathematical topics related to the Fibonacci numbers, published four times per year. It is the primary publication of The Fibonacci Association, which has published it since 1963. Its founding ...

* Finite Fields and Their Applications * Geombinatorics *

Graphs and Combinatorics ''Graphs and Combinatorics'' (ISSN 0911-0119, abbreviated ''Graphs Combin.'') is a peer-reviewed academic journal in graph theory, combinatorics, and discrete geometry published by Springer Japan. Its editor-in-chief is Katsuhiro Ota of Keio Unive ...

* Integers, Electronic Journal of Combinatorial Number Theory *

Journal of Algebraic Combinatorics ''Journal of Algebraic Combinatorics'' is a peer-reviewed scientific journal covering algebraic combinatorics Algebraic combinatorics is an area of mathematics that employs methods of abstract algebra, notably group theory and representation t ...

* Journal of Automata, Languages and Combinatorics * Journal of Combinatorial Designs * Journal of Combinatorial Mathematics and Combinatorial Computing * Journal of Combinatorial Optimization *

Journal of Combinatorial Theory, Series A The ''Journal of Combinatorial Theory'', Series A and Series B, are mathematical journals specializing in combinatorics and related areas. They are published by Elsevier. ''Series A'' is concerned primarily with structures, designs, and applicati ...

Journal of Combinatorial Theory, Series B The ''Journal of Combinatorial Theory'', Series A and Series B, are mathematical journals specializing in combinatorics and related areas. They are published by Elsevier. ''Series A'' is concerned primarily with structures, designs, and applicati ...

* Journal of Complexity *

Journal of Cryptology The ''Journal of Cryptology'' () is a scientific journal in the field of cryptology and cryptography. The journal is published quarterly by the International Association for Cryptologic Research. Its editor-in-chief is Vincent Rijmen Vincent R ...

Journal of Graph Algorithms and Applications The ''Journal of Graph Algorithms and Applications'' is an open access peer-reviewed scientific journal covering the subject of graph algorithms and graph drawing. The journal was established in 1997 and the editor-in-chief is Giuseppe Liotta (Univ ...

Journal of Graph Theory The ''Journal of Graph Theory'' is a peer-reviewed mathematics journal specializing in graph theory and related areas, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs. Th ...

* Journal of Integer Sequences (Electronic) * Journal of Mathematical Chemistry * Online Journal of Analytic Combinatorics * Optimization Methods and Software * The Ramanujan Journal *

Séminaire Lotharingien de Combinatoire The ''Séminaire Lotharingien de Combinatoire'' (English: ''Lotharingian Seminar of Combinatorics'') is a peer-reviewed academic journal specialising in combinatorial mathematics, named after Lotharingia. It has existed since 1980 as a regular j ...

SIAM Journal on Discrete Mathematics '' SIAM Journal on Discrete Mathematics'' is a peer-reviewed mathematics journal published quarterly by the Society for Industrial and Applied Mathematics (SIAM). The journal includes articles on pure and applied discrete mathematics. It was esta ...

Prizes

Euler Medal The Institute of Combinatorics and its Applications (ICA) is an international scientific organization formed in 1990 to increase the visibility and influence of the combinatorial community. In pursuit of this goal, the ICA sponsors conferences, ...

European Prize in Combinatorics The European Prize in Combinatorics is a prize for research in combinatorics, a mathematical discipline, which is awarded biennially at Eurocomb, the European conference on combinatorics, graph theory, and applications.. The prize was first awarde ...

Fulkerson Prize The Fulkerson Prize for outstanding papers in the area of discrete mathematics is sponsored jointly by the Mathematical Optimization Society (MOS) and the American Mathematical Society (AMS). Up to three awards of $1,500 each are presented at e ...

* König Prize * Pólya Prize

References

External links

Combinatorics
a

MathWorld ''MathWorld'' is an online mathematics reference work, created and largely written by Eric W. Weisstein. It is sponsored by and licensed to Wolfram Research, Inc. and was partially funded by the National Science Foundation's National Science ...

article with many references.
Combinatorics
from a ''MathPages.com'' portal.
The Hyperbook of Combinatorics
a collection of math articles links.
The Two Cultures of Mathematics
by W. T. Gowers, article on problem solving vs theory building {{Outline footer

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. It is closely related to many other areas of mathematics and has many a ...