Essence of combinatorics

Main article: Combinatorics

Combinatorics

Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size , deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria ,...

• Matroid
  Matroid
  In combinatorics, a branch of mathematics, a matroid or independence structure is a structure that captures the essence of a notion of "independence" that generalizes linear independence in vector spaces....
  
  
• Greedoid
  Greedoid
  In combinatorics, a greedoid is a type of set system. It arises from the notion of the matroid, which was originally introduced by Whitney in 1935 to study planar graphs and was later used by Edmonds to characterize a class of optimization problems that can be solved by greedy algorithms...
  
  
• Ramsey theory
  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...
  
  
  • Van der Waerden's theorem
  • Hales–Jewett theorem
    Hales–Jewett theorem
    In mathematics, the Hales–Jewett theorem is a fundamental combinatorial result of Ramsey theory, concerning the degree to which high-dimensional objects must necessarily exhibit some combinatorial structure; it is impossible for such objects to be "completely random".An informal geometric statement...
    
    
  • Umbral calculus
    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 and are sometimes called Blissard's symbolic method...
    
    , binomial type polynomial sequences
• Combinatorial species
  Combinatorial species
  In combinatorial mathematics, the theory of combinatorial species is an abstract, systematic method for analysing discrete structures in terms of generating functions. Examples of discrete structures are graphs, permutations, trees, and so on; each of these has an associated generating function...
  
  

Branches of combinatorics

• Algebraic 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 algebra....
  
  
• Analytic combinatorics
  Analytic combinatorics
  Analytic combinatorics is a branch of combinatorics that describes combinatorial classes using generating functions, with formal power series that often correspond to analytic functions....
  
  
• Arithmetic combinatorics
  Arithmetic combinatorics
  Arithmetic combinatorics arose out of the interplay between number theory, combinatorics, ergodic theory and harmonic analysis. It is about combinatorial estimates associated with arithmetic operations...
  
  
• Combinatorics on words
  Combinatorics on words
  Combinatorics on words is a branch of mathematics which applies combinatorics to words and formal languages. The study of combinatorics on words arose independently within several branches of mathematics, e.g. number theory, group theory and probability...
  
  
• Combinatorial design theory
• Enumerative combinatorics
  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...
  
  
• Extremal combinatorics
  Extremal combinatorics
  Extremal combinatorics is a field of combinatorics, which is itself a part of mathematics. Extremal combinatorics studies how large or how small a collection of finite objects can be, if it has to satisfy certain restrictions.For example, how many people can we invite to a party where among each...
  
  
• Geometric combinatorics
  Geometric combinatorics
  Geometric combinatorics is a branch of mathematics in general and combinatorics in particular. It includes a number of subareas such as polyhedral combinatorics , convex geometry , and discrete geometry, which in turn has many applications to computational geometry...
  
  
• Graph theory
  Graph theory
  In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context refers to a collection of vertices or 'nodes' and a collection of edges that connect pairs of...
  
  
• Infinitary combinatorics
  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
• Order theory
  Order theory
  Order theory is a branch of mathematics which investigates our 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 introduces the field and gives some basic definitions...
  
  
• Partition theory
• Probabilistic combinatorics
  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 from a specified class, the probability that the...
  
  
• Topological combinatorics
  Topological combinatorics
  The discipline of combinatorial topology used combinatorial concepts in topology and in the early 20th century this gradually turned into the field of algebraic topology....
  
  

Multi-disciplinary fields that include combinatorics

• Coding theory
  Coding theory
  Coding theory is the study of the properties of codes and their fitness for a specific application. Codes are used for data compression, cryptography, error-correction and more recently also for network coding...
  
  
• Combinatorial optimization
  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. In many such problems, exhaustive search is not feasible...
  
  
• Combinatorics and dynamical systems
  Combinatorics and dynamical systems
  The mathematical disciplines of combinatorics and dynamical systems interact in a number of ways. The ergodic theory of dynamical systems has recently been used to prove combinatorial theorems about number theory which has given rise to the field of arithmetic combinatorics. Also dynamical systems...
  
  
• Combinatorics and physics
  Combinatorics and physics
  Combinatorial physics or physical combinatorics is the area of interaction between physics and combinatorics."Combinatorial Physics is an emerging area which unites combinatorial and discrete mathematical techniques applied to theoretical physics, especially Quantum Theory."."Physical combinatorics...
  
  
• Discrete geometry
  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 geometric objects, such as points, lines, planes, circles,...
  
  
• Phylogenetics
  Phylogenetics
  In biology, phylogenetics is the study of evolutionary relatedness among groups of organisms , which is discovered through molecular sequencing data and morphological data matrices...
  
  

General combinatorial principles and methods

• Fundamental theorem of combinatorial enumeration
  Fundamental theorem of combinatorial enumeration
  The fundamental theorem of combinatorial enumeration is a theorem in combinatorics that solves the enumeration problem of labelled and unlabelled combinatorial classes.The unlabelled case is based on the Pólya enumeration theorem....
  
  
• Combinatorial principles
  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. Bijective proofs are utilized to demonstrate that two sets...
  
  
• Trial and error
  Trial and error
  Trial and error, or trial by error, is a general method of problem solving, fixing things, or for obtaining knowledge."Learning doesn't happen from failure itself but rather from analyzing the failure, making a change, and then trying again."...
  
  , brute force search, bogosort
  Bogosort
  In computer science, bogosort is a particularly ineffective sorting algorithm based on the generate and test paradigm. It is not useful for sorting, but may be used for educational purposes, to contrast it with other more realistic algorithms; it has also been used as an example in logic programming...
  
  , British Museum algorithm
  British Museum algorithm
  The British Museum algorithm is a general approach to find 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 are enormous....
  
  
• Pigeonhole principle
• Method of distinguished element
  Method of distinguished element
  In enumerative combinatorial mathematics, identities are sometimes established by arguments that rely on singling out one "distinguished element" of a set.-Examples:...
  
  
• Mathematical induction
  Mathematical induction
  Mathematical induction is a method of mathematical proof typically used to establish that a given statement is true of all natural numbers...
  
  
• Recurrence relation
  Recurrence relation
  In mathematics, a recurrence relation is an equation that recursively defines a sequence, once one or more initial terms are given: each further term of the sequence is defined as a function of the preceding terms....
  
  , telescoping series
• Generating function
  Generating function
  In mathematics, a generating function is a formal power series in one indeterminate, whose coefficients encode information about a sequence of numbers an that is indexed by the natural numbers. Generating functions were first introduced by Abraham de Moivre in 1730, in order to solve the general...
  
  s as an application of formal power series
  Formal power series
  In mathematics, formal power series are a generalization of polynomials as formal objects, where the number of terms is allowed to be infinite; this implies giving up the possibility to substitute arbitrary values for indeterminates...
  
  
  • Schrödinger method
    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.SupposeX_1,\dots,X_n \,...
    
    
  • exponential generating function
  • Stanley's reciprocity theorem
    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 and the generating function of the cone's interior.A rational cone is the set of all...
    
    
• Binomial coefficient
  Binomial coefficient
  In mathematics, binomial coefficients are a family of positive integers that occur as coefficients in the binomial theorem. They are indexed by two nonnegative integers; the binomial coefficient indexed by n and k is usually written \tbinom nk , and it is the coefficient of the x k term in...
  
  s and their properties
• Combinatorial proof
  Combinatorial proof
  In mathematics, the term combinatorial proof is often used to mean either of two types of proof of an identity in enumerative combinatorics that either states that two sets of combinatorial configurations, depending on one or more parameters, have the same number of elements , or gives a formula...
  
  
  • Double counting (proof technique)
    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...
    
    
  • Bijective proof
    Bijective proof
    In combinatorics, bijective proof is a proof technique that finds a bijective function f : A → B between two sets A and B, thus proving that they have the same number of elements, |A| = |B|. One place the technique is useful is where we wish to know the size of A, but can find no direct way of...
    
    
• Inclusion-exclusion principle
  Inclusion-exclusion principle
  In combinatorics, the inclusion–exclusion principle is an equation relating the sizes of two sets and their union...
  
  
• Möbius inversion formula
  Möbius inversion formula
  In mathematics, the classic Möbius inversion formula was introduced into number theory during the 19th century by August Ferdinand Möbius. Other Möbius inversion formulas are obtained when different local finite partially ordered sets replace the classic case of the natural numbers ordered by...
  
  
• Parity, even and odd permutations
  Even and odd permutations
  In mathematics, when X is a finite set of at least two elements, the permutations of X fall into two classes of equal size: the even permutations and the odd permutations...
  
  
• Combinatorial Nullstellensatz
• Incidence algebra
  Incidence algebra
  In order theory, a field of mathematics, an incidence algebra is an associative algebra, defined for any locally finite partially ordered setand commutative ring with unity.-Definition:...
  
  
• Greedy algorithm
  Greedy algorithm
  A greedy algorithm is any algorithm that follows the problem solving heuristic of making the locally optimal choice at each stagewith the hope of finding the global optimum....
  
  
• Divide and conquer algorithm
  Divide and conquer algorithm
  In computer science, divide and conquer is an important algorithm design paradigm based on multi-branched recursion. A divide and conquer algorithm works by recursively breaking down a problem into two or more sub-problems of the same type, until these become simple enough to be solved directly...
  
  
  • Akra-Bazzi method
    Akra-Bazzi method
    In computer science, the Akra–Bazzi method, or Akra–Bazzi theorem, is used to analyze the asymptotic behavior of the mathematical recurrences that appear in the analysis of divide and conquer algorithms where the sub-problems have substantially different sizes...
    
    
• Dynamic programming
  Dynamic programming
  In mathematics and computer science, dynamic programming is a method for solving complex problems by breaking them down into simpler subproblems. It is applicable to problems exhibiting the properties of overlapping subproblems which are only slightly smaller and optimal substructure...
  
  
• Branch and bound
  Branch and bound
  Branch and bound is a general algorithm for finding optimal solutions of various optimization problems, especially in discrete and combinatorial optimization...
  
  
• Birthday attack
  Birthday attack
  A birthday attack is a type of cryptographic attack that exploits the mathematics behind the birthday problem in probability theory. This attack can be used to abuse communication between two or more parties...
  
  , birthday paradox
  Birthday paradox
  In probability theory, the birthday problem or birthday paradox pertains to the probability that, in a set of n randomly chosen people, some pair of them will have the same birthday. By the pigeonhole principle, the probability reaches 100% when the number of people reaches 366. However, 99%...
  
  
• Floyd's cycle-finding algorithm
  Floyd's cycle-finding algorithm
  In computer science, cycle detection is the algorithmic problem of finding a cycle in a sequence of iterated function values.For any function ƒ that maps a finite set S to itself, and any initial value x0 in S, the sequence of iterated function values x_0,\ x_1=f,\ x_2=f,\ \dots,\ x_i=f,\ \dotsmust...
  
  
• Reduction to linear algebra
  Linear algebra
  Linear algebra is a branch of mathematics that studies vector spaces, also called linear spaces, along with linear functions that input one vector and output another. Such functions are called linear maps and can be represented by matrices if a basis is given. Thus matrix theory is often...
  
  
• Sparsity
  Sparse matrix
  In the subfield of numerical analysis, a sparse matrix is a matrix populated primarily with zeros . The term itself was coined by Harry M. Markowitz....
  
  
• Weight function
  Weight function
  A weight function is a mathematical device used when performing a sum, integral, or average in order to give some elements more "weight" or influence on the result than other elements in the same set. They occur frequently in statistics and analysis, and are closely related to the concept of a...
  
  
• Minimax algorithm
  • Alpha-beta pruning
    Alpha-beta pruning
    Alpha-beta pruning is a search algorithm which 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
  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 from a specified class, the probability that the...
  
  
• Sieve methods
• Analytic combinatorics
  Analytic combinatorics
  Analytic combinatorics is a branch of combinatorics that describes combinatorial classes using generating functions, with formal power series that often correspond to analytic functions....
  
  
• Symbolic combinatorics
  Symbolic combinatorics
  In mathematics, symbolic combinatorics is one of the many techniques of counting combinatorial objects. It uses the internal structure of the objects to derive formulas for their generating functions. This particular theory is due to Philippe Flajolet and Robert Sedgewick. This article describes...
  
  
• Combinatorial class
  Combinatorial class
  In combinatorics, a combinatorial class is an equivalence class of sets that have the same counting sequence. Although the elements of these equivalent sets may have very different definitions and semantics, combinatorics is concerned only with the number of elements of a given size...
  
  
• Exponential formula
  Exponential formula
  In combinatorial mathematics, the exponential formula states that the exponential generating function for structures on finite sets is the exponential of the exponential generating function for connected structures.The exponential formula is a power-series version of a special case of Faà di...
  
   
• Twelvefold way
  Twelvefold way
  In combinatorics, the twelvefold way is a name given to 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...
  
   
• MacMahon Master theorem
  MacMahon Master theorem
  The MacMahon Master theorem is a result in enumerative combinatorics and linear algebra, both branches of mathematics. It was discovered by Percy MacMahon and proved in his monograph Combinatory analysis...
  
   

Data structure concepts

• Data structure
  Data structure
  In computer science, a data structure is a particular way of storing and organizing data in a computer so that it can be used efficiently.Different kinds of data structures are suited to different kinds of applications, and some are highly specialized to specific tasks...
  
  
  • Data type
    Data type
    In computer programming, a data type is a classification identifying one of various types of data, such as floating-point, integer, or Boolean, that determines the possible values for that type; the operations that can be done on values of that type; the meaning of the data; and the way values of...
    
    
  • Abstract data type
    Abstract data type
    In computing, an abstract data type is a mathematical model for a certain class of data structures that have similar behavior; or for certain data types of one or more programming languages that have similar semantics...
    
    
  • Algebraic data type
    Algebraic data type
    In computer programming, particularly functional programming and type theory, an algebraic data type is a datatype each of whose values is data from other datatypes wrapped in one of the constructors of the datatype. Any wrapped datum is an argument to the constructor...
    
    
  • Composite type
    Composite type
    In computer science, a composite data type is any data type which can be constructed in a program using its programming language's primitive data types and other composite types...
    
    
• Array
• Associative array
  Associative array
  In computer science, an associative array is an abstract data type composed of a collection of pairs, such that each possible key appears at most once in the collection....
  
  
• Deque
  Deque
  In computer science, a double-ended queue is an abstract data structure that implements a queue for which elements can only be added to or removed from the front or back...
  
  
• List
  • Linked list
    Linked list
    In computer science, a linked list is a data structure consisting of a group of nodes which together represent a sequence. Under the simplest form, each node is composed of a datum and a reference to the next node in the sequence; more complex variants add additional links...
    
    
• Queue
  • Priority queue
    Priority queue
    A priority queue is an abstract data type in computer programming.It is exactly like a regular queue or stack data structure, but additionally, each element is associated with a "priority"....
    
    
• Skip list
  Skip list
  A skip list is a data structure for storing a sorted list of items using a hierarchy of linked lists that connect increasingly sparse subsequences of the items...
  
  
• Stack
  Stack (data structure)
  In computer science, a stack is a last in, first out abstract data type and linear data structure. A stack can have any abstract data type as an element, but is characterized by only three fundamental operations: push, pop and stack top. The push operation adds a new item to the top of the stack,...
  
  
• Tree data structure
• Automatic garbage collection
  Garbage collection (computer science)
  In computer science, garbage collection is a form of automatic memory management. The garbage collector, or just collector, attempts to reclaim garbage, or memory occupied by objects that are no longer in use by the program...
  
  

Problem solving as an art

• Heuristic
  Heuristic
  Heuristic refers to experience-based techniques for problem solving, learning, and discovery. Heuristic methods are used to speed up the process of finding a satisfactory solution, where an exhaustive search is impractical...
  
  
• Inductive reasoning
  Inductive reasoning
  Inductive reasoning, also known as induction or inductive logic, is a kind of reasoning that constructs or evaluates propositions that are abstractions of observations. It is commonly construed as a form of reasoning that makes generalizations based on individual instances...
  
  
• How to Solve It
  How to Solve It
  How to Solve It 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:...
  
  
• Creative problem solving
  Creative problem solving
  Creative problem solving is the mental process of creating a solution to a problem. It is a special form of problem solving in which the solution is independently created rather than learned with assistance.Creative problem solving always involves creativity....
  
  

Living with large numbers

• Names of large numbers
  Names of large numbers
  This article lists and discusses the usage and derivation of names of large numbers, together with their possible extensions.The following table lists those names of large numbers which are found in many English dictionaries and thus have a special claim to being "real words"...
  
  , long scale
  Long and short scales
  The long and short scales are two of several different large-number naming systems used throughout the world for integer powers of ten. Many countries, including most in continental Europe, use the long scale whereas most English-speaking countries use the short scale...
  
  
• History of large numbers
  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....
  
  
• Graham's number
  Graham's number
  Graham's number, named after Ronald Graham, is a large number that is an upper bound on the solution to a certain problem in Ramsey theory.The number gained a degree of popular attention when Martin Gardner described it in the "Mathematical Games" section of Scientific American in November 1977,...
  
  
• Moser's number
• Skewes' number
• Large number notations
  • Conway chained arrow notation
    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 → 3 → 4 → 5 → 6.As with most...
    
    
  • Hyper4
  • Knuth's up-arrow notation
    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. It is closely related to the Ackermann function and especially to the hyperoperation sequence. The idea is based on the fact that multiplication can be viewed as iterated...
    
    
  • Moser polygon notation
  • Steinhaus polygon notation
• Large number effects
  • Exponential growth
    Exponential growth
    Exponential growth occurs when the growth rate of a mathematical function is proportional to the function's current value...
    
    
  • Combinatorial explosion
    Combinatorial explosion
    In administration and computing, a combinatorial explosion is the rapidly accelerating increase in lines of communication as organizations are added in a process...
    
    
  • Branching factor
    Branching factor
    In computing, tree data structures, and game theory, the branching factor is the number of children at each node. If this value is not uniform, an average branching factor can be calculated....
    
    
  • Granularity
    Granularity
    Granularity is the extent to which a system is broken down into small parts, either the system itself or its description or observation. It is the "extent to which a larger entity is subdivided...
    
    
  • Curse of dimensionality
    Curse of dimensionality
    The curse of dimensionality refers to various phenomena that arise when analyzing and organizing high-dimensional spaces that do not occur in low-dimensional settings such as the physical space commonly modeled with just three dimensions.There are multiple phenomena referred to by this name in...
    
    
  • Concentration of measure
    Concentration of measure
    In mathematics, concentration of measure 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 variable that depends in a Lipschitz way on many independent variables ...
    
    

Persons influential in the field of combinatorics

• Noga Alon
  Noga Alon
  Noga Alon is an Israeli mathematician noted for his contributions to combinatorics and theoretical computer science, having authored hundreds of papers.- Academic background :...
  
  
• George Andrews
• Eric Temple Bell
  Eric Temple Bell
  Eric Temple Bell , was a mathematician and science fiction author born in Scotland who lived in the U.S. for most of his life...
  
  
• Claude Berge
  Claude Berge
  Claude Berge was a French mathematician, recognized as one of the modern founders of combinatorics and graph theory. He is particularly remembered for his famous conjectures on perfect graphs and for Berge's lemma, which states that a matching M in a graph G is maximum if and only if there is in...
  
  
• Belá Bollobás
  Béla Bollobás
  Béla Bollobás FRS is a Hungarian-born British mathematician who has worked in various areas of mathematics, including functional analysis, combinatorics, graph theory and percolation. As a student, he took part in the first three International Mathematical Olympiads, winning two gold medals...
  
  
• Peter Cameron
  Peter Cameron (mathematician)
  Peter Jephson Cameron is an Australian mathematician who works ingroup theory, combinatorics, coding theory, and model theory. He is currently Professor of Mathematics at Queen Mary, University of London....
  
  
• Louis Comtet
• John Horton Conway
  John Horton Conway
  John Horton Conway is a prolific mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory...
  
  
  • On Numbers and Games
    On Numbers and Games
    On Numbers and Games is a mathematics book by John Horton Conway. The book is a serious mathematics book, written by a pre-eminent mathematician, and is directed at other mathematicians...
    
    
  • Winning Ways for your Mathematical Plays
    Winning Ways for your Mathematical Plays
    Winning Ways for your Mathematical Plays by Elwyn R. Berlekamp, John H. Conway, and Richard K. Guy is a compendium of information on mathematical games...
    
    
• Persi Diaconis
  Persi Diaconis
  Persi Warren Diaconis is an American mathematician and former professional magician. He is the Mary V. Sunseri Professor of Statistics and Mathematics at Stanford University....
  
  
• Ada Dietz
  Ada Dietz
  Ada K. Dietz was an American weaver best known for her 1949 monograph Algebraic Expressions in Handwoven Textiles, which defines a novel method for generating weaving patterns based on algebraic patterns. Her method employs the expansion of multivariate polynomials to devise a weaving scheme...
  
  
• Paul Erdős
  Paul Erdos
  Paul Erdős was a Hungarian mathematician. Erdős published more papers than any other mathematician in history, working with hundreds of collaborators. He worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory...
  
  
  • Erdős conjecture
    Erdos conjecture
    The prolific mathematician Paul Erdős and his various collaborators made many famous mathematical conjectures, over a wide field of subjects.Some of these are the following:* The Cameron–Erdős conjecture on sum-free sets of integers, proved by Ben Green....
    
    
• Solomon Golomb
• Ben Green
• Tim Gowers
  William Timothy Gowers
  William Timothy Gowers FRS is a British mathematician. He is a Royal Society Research Professor at the Department of Pure Mathematics and Mathematical Statistics at Cambridge University, where he also holds the Rouse Ball chair, and is a Fellow of Trinity College...
  
  
• Gyula O. H. Katona
  Gyula O. H. Katona
  Gyula O. H. Katona is a Hungarian mathematician known for his work in combinatorial set theory, and especially for the Kruskal–Katona theorem and his elegant proof of the Erdős–Ko–Rado theorem...
  
  
• Imre Leader
  Imre Leader
  Imre Bennett Leader is a British mathematician and Professor of Pure Mathematics, specifically combinatorics, at the University of Cambridge....
  
  
• László Lovász
  László Lovász
  László Lovász is a Hungarian mathematician, best known for his work in combinatorics, for which he was awarded the Wolf Prize and the Knuth Prize in 1999, and the Kyoto Prize in 2010....
  
  
• Luke Pebody
  Luke Pebody
  Luke Thomas Pebody is a mathematician who solved the necklace problem. Educated at Rugby School, and competing three times in the International Mathematical Olympiad, Luke Pebody was admitted to Cambridge University at the age of 14 to read mathematics...
  
  
• George Pólya
  George Pólya
  George Pólya 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 fundamental contributions to combinatorics, number theory, numerical analysis and probability theory...
  
  
• Gian-Carlo Rota
  Gian-Carlo Rota
  Gian-Carlo Rota was an Italian-born American mathematician and philosopher.-Life:Rota was born in Vigevano, Italy...
  
  
• Cecil C. Rousseau
• Herbert Ryser
• Dick Schelp
• Vera T. Sós
  Vera T. Sós
  Vera T. Sós is a Hungarian mathematician, specializing in number theory and combinatorics. She was a student and close collaborator of both Paul Erdős and Alfréd Rényi. She also collaborated frequently with her husband Paul Turán, the famous analyst, number theorist, and combinatorist...
  
  
• Joel Spencer
  Joel Spencer
  Joel Spencer 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 supervision of Andrew Gleason...
  
  
• Emanuel Sperner
  Emanuel Sperner
  Emanuel Sperner was a German mathematician, best known for two theorems. He was born in Waltdorf , and died in Sulzburg-Laufen, Germany. He was a student at Hamburg University where his advisor was Wilhelm Blaschke...
  
  
• Richard P. Stanley
  Richard P. Stanley
  Richard Peter Stanley is the Norman Levinson Professor of Applied Mathematics at the Massachusetts Institute of Technology, in Cambridge, Massachusetts. He received his Ph.D. at Harvard University in 1971 under the supervision of Gian-Carlo Rota...
  
  
• Endre Szemerédi
  Endre Szemerédi
  Endre Szemerédi is a Hungarian mathematician, working in the field of combinatorics and theoretical computer science. He is the State of New Jersey Professor of computer science at Rutgers University since 1986...
  
  
• Terence Tao
  Terence Tao
  Terence Chi-Shen Tao FRS is an Australian mathematician working primarily on harmonic analysis, partial differential equations, combinatorics, analytic number theory and representation theory...
  
  
• Carsten Thomassen
  Carsten Thomassen
  Carsten Thomassen is a Danish mathematician. He has been a Professor of Mathematics at the Technical University of Denmark since 1981, and since 1990 a member of the Royal Danish Academy of Sciences and Letters. His research concerns discrete mathematics and more specifically graph...
  
  
• Jacques Touchard
  Jacques Touchard
  Jacques Touchard was a French mathematician. In 1953, he proved that an odd perfect number must be of the form 12k + 1 or 36k + 9. In combinatorics and probability theory, he introduced the Touchard polynomials...
  
  
• Bartel Leendert van der Waerden
  Bartel Leendert van der Waerden
  Bartel Leendert van der Waerden was a Dutch mathematician and historian of mathematics....
  
  
• Richard Wilson
  R. M. Wilson
  Richard Michael Wilson is a mathematician and a professor at the California Institute of Technology. Wilson and D. K. Ray-Chaudhuri, , solved Kirkman's schoolgirl problem in 1968. Wilson is known for his work in combinatorial mathematics.-References:*...
  
  
• Herbert Wilf
  Herbert Wilf
  Herbert Saul Wilf is 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 Pennsylvania. He has written numerous books and research papers...
  
  
• Doron Zeilberger
  Doron Zeilberger
  Doron Zeilberger is an Israeli mathematician, known for his work in combinatorics.He is a Board of Governors Professor of Mathematics at Rutgers University...
  
  

Journals

• Annals of Combinatorics
• Ars Combinatoria
• Australasian Journal of Combinatorics
• Bulletin of the Institute of Combinatorics and Its Applications
• Combinatorica
  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 honorary editor-in-chief. The current editors-in-chief are László...
  
  
• Combinatorics, Probability and Computing
• Computational Complexity
• Designs, Codes and Cryptography
• Discrete and Computational Geometry
  Discrete and Computational Geometry
  Discrete & Computational Geometry is a peer-reviewed mathematics journal published quarterly by Springer. Founded in 1986, the journal publishes articles on in discrete geometry and computational geometry....
  
  
• Discrete Applied Mathematics
• Discrete Mathematics
  Discrete mathematics
  Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics – such as integers, graphs, and statements in logic – do not...
  
  
• Discrete Mathematics & Theoretical Computer Science
• Discrete Optimization
• Discussiones Mathematicae Graph Theory
• Electronic Journal of Combinatorics
• European Journal of Combinatorics
• The Fibonacci Quarterly
  Fibonacci Quarterly
  As the primary publication of The Fibonacci Association, The Fibonacci Quarterly provides a focus for worldwide interest in the Fibonacci number sequence and related mathematics. Published since 1963, its founding editors were Verner Emil Hoggatt, Jr. and Alfred Brousseau...
  
  
• Finite Fields and Their Applications
• Geombinatorics
  Geombinatorics
  Geombinatorics is a mathematical research journal founded by Alexander Soifer and published by the University of Colorado, USA, since 1991 under an international board of editors...
  
  
• Graphs and Combinatorics
• Integers, Electronic Journal of Combinatorial Number Theory
• Journal of Algebraic Combinatorics
  Journal of Algebraic Combinatorics
  Journal of Algebraic Combinatorics is an international mathematical journal dedicated to the field of algebraic combinatorics. It is published bimonthly by Springer-Verlag.- External links :*...
  
  
• Journal of Automata, Languages and Combinatorics
  Journal of Automata, Languages and Combinatorics
  The Journal of Automata, Languages and Combinatorics is a peer-reviewed scientific journal of computer science, edited by Jürgen Dassow. It was established in 1965 as the Journal of Information Processing and Cybernetics/Elektronische Informationsverarbeitung und Kybernetik and obtained its current...
  
  
• Journal of Combinatorial Designs
• Journal of Combinatorial Mathematics and Combinatorial Computing
• Journal of Combinatorial Optimization
• Journal of Combinatorial Theory, Series A
• Journal of Combinatorial Theory, Series B
• Journal of Complexity
• Journal of Cryptology
• Journal of Graph Algorithms and Applications
  Journal of Graph Algorithms and Applications
  The Journal of Graph Algorithms and Applications is an open access electronically published academic journal devoted to the subject of graph algorithms and graph drawing....
  
  
• Journal of Graph Theory
  Journal of Graph Theory
  The Journal of Graph Theory is a mathematics journal specializing in graph theory and related areas, such as other branches of combinatorics and the interaction of graph theory with other mathematical sciences...
  
  
• 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
• SIAM Journal on Discrete Mathematics

See also

• List of factorial and binomial topics
• List of partition topics
• List of permutation topics
• List of puzzle topics.
• List of formal language and literal string topics

External links

• Combinatorics, a MathWorld
  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 Digital Library grant to the University of Illinois at...
  
  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