Outline of combinatorics

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

Persons influential in the field of 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