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

Essence of combinatorics

• Matroid

• Greedoid

Ramsey theory

• Van der Waerden's theorem

• Hales–Jewett theorem

• Umbral calculus, binomial type polynomial sequences

• Combinatorial species

Branches of combinatorics

• Algebraic combinatorics

• Analytic combinatorics

• Arithmetic combinatorics

• Combinatorics on words

• Combinatorial design theory

• Enumerative combinatorics

• Extremal combinatorics

• Geometric combinatorics

• Graph theory

• Infinitary combinatorics

• Matroid theory

• Order theory

• Partition theory

• Probabilistic combinatorics

• Topological combinatorics

Multi-disciplinary fields that include combinatorics

• Coding theory

• Combinatorial optimization

• Combinatorics and dynamical systems

• Combinatorics and physics

• Discrete geometry

• Finite geometry

• Phylogenetics

History of combinatorics

History of combinatorics

General combinatorial principles and methods

• Combinatorial principles

• Trial and error, brute-force search, bogosort, British Museum algorithm

• Pigeonhole principle

• Method of distinguished element

• Mathematical induction

• Recurrence relation, telescoping series

Generating functions as an application of formal power series

• Cyclic sieving

• Schrödinger method

• Exponential generating function

• Stanley's reciprocity theorem

• Binomial coefficients and their properties

Combinatorial proof

• Double counting (proof technique)

• Bijective proof

• Inclusion–exclusion principle

• Möbius inversion formula

• Parity, even and odd permutations

• Combinatorial Nullstellensatz

• Incidence algebra

• Greedy algorithm

Divide and conquer algorithm

• Akra–Bazzi method

• Dynamic programming

• Branch and bound

• Birthday attack, birthday paradox

• Floyd's cycle-finding algorithm

• Reduction to linear algebra

• Sparsity

• Weight function

Minimax algorithm

• Alpha–beta pruning

• Probabilistic method

• Sieve methods

• Analytic combinatorics

• Symbolic combinatorics

• Combinatorial class

• Exponential formula

• Twelvefold way

• MacMahon Master theorem

Data structure concepts

Data structure

• Data type

• Abstract data type

• Algebraic data type

• Composite type

• Array

• Associative array

• Deque

List

• Linked list

Queue

• Priority queue

• Skip list

• Stack

• Tree data structure

• Automatic garbage collection

Problem solving as an art

• Heuristic

• Inductive reasoning

• How to Solve It

• Creative problem solving

• Morphological analysis (problem-solving)

Living with large numbers

• Names of large numbers, long scale

• History of large numbers

• Graham's number

• Moser's number

• Skewes' number

Large number notations

• Conway chained arrow notation

• Hyper4

• Knuth's up-arrow notation

• Moser polygon notation

• Steinhaus polygon notation

Large number effects

• Exponential growth

• Combinatorial explosion

• Branching factor

• Granularity

• Curse of dimensionality

• Concentration of measure

People in combinatorics

• Noga Alon

• George Andrews

• József Beck

• Eric Temple Bell

• Claude Berge

• Béla Bollobás

• Peter Cameron

• Louis Comtet

John Horton Conway

• On Numbers and Games

• Winning Ways for your Mathematical Plays

• Persi Diaconis

• Ada Dietz

Paul Erdős

• Erdős conjecture

• Philippe Flajolet

• Solomon Golomb

• Ron Graham

• Ben Green

• Tim Gowers

• Jeff Kahn

• Gil Kalai

• Gyula O. H. Katona

• Daniel J. Kleitman

• Imre Leader

• László Lovász

• Fedor Petrov

• George Pólya

• Vojtěch Rödl

• Gian-Carlo Rota

• Cecil C. Rousseau

• H. J. Ryser

• Dick Schelp

• Vera T. Sós

• Joel Spencer

• Emanuel Sperner

• Richard P. Stanley

• Benny Sudakov

• Endre Szemerédi

• Terence Tao

• Carsten Thomassen

• Jacques Touchard

• Pál Turán

• Bartel Leendert van der Waerden

• Herbert Wilf

• Richard Wilson

• Doron Zeilberger

Combinatorics scholars

• :Category:Combinatorialists

Journals

• Advances in Combinatorics

• Annals of Combinatorics

• Ars Combinatoria

• Australasian Journal of Combinatorics

• Bulletin of the Institute of Combinatorics and Its Applications

• Combinatorica

• Combinatorics, Probability and Computing

• Computational Complexity

• Designs, Codes and Cryptography

• Discrete Analysis

• Discrete & Computational Geometry

• Discrete Applied Mathematics

• Discrete Mathematics

• Discrete Mathematics & Theoretical Computer Science

• Discrete Optimization

• Discussiones Mathematicae Graph Theory

• Electronic Journal of Combinatorics

• European Journal of Combinatorics

• The Fibonacci Quarterly

• Finite Fields and Their Applications

• Geombinatorics

• Graphs and Combinatorics

• Integers, Electronic Journal of Combinatorial Number Theory

• Journal of Algebraic Combinatorics

• 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

• Journal of Combinatorial Theory, Series B

• Journal of Complexity

• Journal of Cryptology

• Journal of Graph Algorithms and Applications

• Journal of Graph Theory

• 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

Prizes

• Euler Medal

• European Prize in Combinatorics

• Fulkerson Prize

• König Prize

• Pólya Prize

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

References

External links

• Combinatorics, a MathWorld 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