# 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