# List of combinatorics topics

This is a**list of combinatorics topics**, by Wikipedia page.

A few decades ago it might have been said that combinatorics is to mathematics roughly what irritable bowel syndrome is to gastroenterology - a way to classify poorly-understood problems, and some standard remedies. Great progress has been made since 1960.

This page is complementary to the list of graph theory topics: graph theory being the part of combinatorial mathematics that is most like a separate discipline. In general, combinatorics is as much about problem solving as theory building.

Since combinatorial mathematics is effectively the environment for the study of data structures in computer science, there are very many topics that arise there. The same could be said for other fields, such as error-correcting codes, bioinformatics.

## General combinatorial principles and methods

To begin with, some general principles:

- Trial and error, brute force search, bogosort
- Pigeonhole principle
- Mathematical induction
- Recurrence relation, telescoping series
- Generating functions as an application of formal power series
- Binomial coefficients and their properties
- Double counting, combinatorial proof
- Inclusion-exclusion principle
- Möbius inversion formula
- Parity, even permutations
- Incidence algebra
- Greedy algorithm
- Divide and conquer
- Dynamic programming
- Branch and bound
- Birthday attack, birthday paradox
- Reduction to linear algebra
- Umbral calculus
- Minimax algorithm
- Probabilistic method
- Sieve methods

## Problem solving as an art

## Some general theories

- Matroid
- Greedoid
- Ramsey theory
- Binomial type polynomial sequences
- Combinatorial species

## Living with large numbers

- Names of large numbers
- Graham's number
- Moser's number
- Skewes' number
*Large number notations**Large number effects*- Combinatorial explosion
- Branching factor
- Granularity
- Curse of dimensionality
- Concentration of measure

## Topics

- (0,1) matrix
- Abstract simplicial complex
- Addition chain
- Almost disjoint sets
- Antichain
- Assignment problem
- Barcode
- Bell polynomials
- Binomial theorem
- Block design
- Boolean satisfiability problem
- Bruck-Chowla-Ryser theorem
- Catalan number
- Cellular automaton
- Collatz conjecture
- Combination
- Combinatorial optimization
- Combinatorial search
- Constraint satisfaction problem
- Cyclic order
- Cyclotomic identity
- Data integrity
- Deadlock
- Derangement
- Dickson's lemma
- Discrete optimization
- Eight queens puzzle
- Entropy coding
- Enumeration
- Erdös-Ko-Rado theorem
- Euler number
- Faà di Bruno's formula;
- Family of sets
- Fifteen puzzle
- Finite geometry
- Finite intersection property
- Floyd's cycle-finding algorithm
- Game theory
- Golomb coding
- Golomb ruler
- Graeco-Latin square
- Gray code
- Hadamard matrix
- Hamming distance
- Hash function
- Hat problem
- Helly family
- Hypergeometric function identities
- Hypergeometric series
- Hypergraph
- Incidence structure
- Integer partition
- Ferrers graph

- Kakeya needle problem
- Knapsack problem
- Lah number
- Large number
- Latin square
- Levenshtein distance
- Lexicographical order
- Lubell-Yamamoto-Meshalkin inequality (known as the
**LYM inequality**) - Lucas chain
- Magic square
- Marriage theorem
- Matroid embedding
- Monge array
- Monomial order
- Moreau's necklace-counting function
- Multiset
- Necklace problem
- Negligible set
- Ordered partition of a set
- Packing problem
- Partition of a set
- Permanent
- Permutation
- Pochhammer symbol
- Polyforms
- Polycubes
- Polyiamonds
- Polyominoes
- Hexominoes
- Pentominoes
- Tetrominoes

- Polysquare puzzle

- Projective plane
- Rubik's cube
- Search algorithm
- Series-parallel networks problem
- Shuffling puzzle
- Sparse matrix, sparse array
- Sperner family
- Sperner's lemma
- Stable marriage problem
- Steiner system
- Stirling number
- String algorithm
- Straddling checkerboard
- Subsequence
- Subset sum problem
- Symmetric functions
- Szeméredi's theorem
- Thue-Morse sequence
- Tower of Hanoi
- Turing tarpit
- Urn problems (probability)
- Weighted round robin
- Wigner-d'Espagnat inequality
- Young tableau

## Data structure concepts

- Data structure
- Array
- Associative array
- Deque
- List
- Queue
- Skip list
- Stack
- Tree data structure
- Automatic garbage collection

## People

- John Conway
- Persi Diaconis
- Paul Erdös
- Solomon Golomb
- George Pólya
- Gian-Carlo Rota
- Emanuel Sperner

## Publications

## See also