- List of combinatorics topics
This is a

**list of**.combinatorics topicsA few decades ago it might have been said that combinatorics is little more than 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 structure s incomputer science , there are very many topics that arise there. The same could be said for other fields, such aserror-correcting code s,bioinformatics .**General combinatorial principles and methods**To begin with, some general principles:

*

Fundamental theorem of combinatorial enumeration

*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 function s as an application offormal power series

**Schrödinger method

**exponential generating function

**Stanley's reciprocity theorem

*Binomial coefficient s 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 tolinear algebra

*Sparsity

*Weight function

*Minimax algorithm

**Alpha-beta pruning

*Probabilistic method

*Sieve methods

*Analytic combinatorics

*Symbolic combinatorics

*Combinatorial class

*Exponential formula

*Twelvefold way Problem solving as an art*

Heuristic

*Inductive reasoning

*"How to Solve It "

*Creative problem solving

*"Art of Problem Solving "**ome general theories***

Matroid

*Greedoid

*Ramsey theory

**Van der Waerden's theorem

**Hales-Jewett theorem

**Umbral calculus ,binomial type polynomial sequences

*Combinatorial species **Living with**large number s*

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 **Topics in combinatorics: alphabetical list****0-9***

Binary matrix (i.e. "(0,1)-matrix")**A***

Abstract simplicial complex

*Addition chain

**Scholz conjecture

*Algebraic combinatorics

*Alternating sign matrix

*Almost disjoint sets

*Antichain

*Arrangement of hyperplanes

*Assignment problem

**Quadratic assignment problem

*Audioactive decay **B***

Barcode

**Matrix code

**QR Code

**Universal Product Code

*Bell polynomials

*Bertrand's ballot theorem

*Binomial theorem

*Block design

**Symmetric balanced incomplete block design (SBIBD)

**Balanced incomplete block design (BIBD)

**Partially balanced incomplete block design (PBIBD)

*Block walking

*Boolean satisfiability problem

**2-satisfiability

**3-satisfiability

*Bracelet (combinatorics)

*Bruck-Chowla-Ryser theorem **C***

Catalan number

*Cellular automaton

**Conway's Game of Life

*Collatz conjecture

*Combinadic

*Combination

*Combinatorial design

*Combinatorial optimization

*Combinatorial search

*Constraint satisfaction problem

*Cycles and fixed points

*Cyclic order

*Cyclic permutation

*Cyclotomic identity **D***

Data integrity

**Alternating bit protocol

**Checksum

**Cyclic redundancy check

***Luhn formula

**Error detection

***Error-detecting code

***Error-detecting system

**Message digest

**Redundancy check

**Summation check

*De Bruijn sequence

*Deadlock

*Delannoy number

**Dining philosophers problem

**Mutual exclusion

**Rendezvous problem

*Derangement

*Dickson's lemma

*Dinitz conjecture

*Discrete optimization

*Dobinski's formula **E***

Eight queens puzzle

*Entropy coding

*Enumeration

**Algebraic enumeration

**Combinatorial enumeration

**Burnside's lemma

*Erdős-Ko-Rado theorem

*Euler number **F***

Faà di Bruno's formula

*Factoradic

*Family of sets

*Faulhaber's formula

*Fifteen puzzle

*Finite geometry

*Finite intersection property **G***

Game theory

**Combinatorial game theory

***Combinatorial game theory (history)

***Combinatorial game theory (pedagogy)

***Star (game)

***Zero game ,fuzzy game

**Dots and Boxes

**Impartial game

***Digital sum

***Nim

***Nimber

***Sprague-Grundy theorem

**Partizan game

**Solved board games

**Col game

**Sim

**Sprouts (game)

**Surreal numbers

**Transposition table

**Black Path Game

**Sylver coinage

*Golomb coding

*Golomb ruler

*Graeco-Latin square

*Gray code **H***

Hadamard matrices

**Complex Hadamard matrices

**Butson-type Hadamard matrices

**Generalized Hadamard matrices

**Regular Hadamard matrices

*Hamming distance

*Hash function

**Hash collision

**Perfect hash function

*Hat problem

*Heilbronn triangle problem

*Helly family

*Hypergeometric function identities

*Hypergeometric series

*Hypergraph **I***

Incidence structure

*Integer partition

**Ferrers graph **K***

Kakeya needle problem

*Kirkman's schoolgirl problem

*Knapsack problem

*Kruskal-Katona theorem **L***

Lagrange inversion theorem

*Lagrange reversion theorem

*Lah number

*Large number

*Latin square

*Levenshtein distance

*Lexicographical order

*Littlewood-Offord problem

*Lubell-Yamamoto-Meshalkin inequality (known as the**LYM inequality**)

*Lucas chain **M***

Magic square

*Marriage theorem

**Perfect matching

*Matroid embedding

*Monge array

*Monomial order

*Moreau's necklace-counting function

*Motzkin number

*Multiplicities of entries in Pascal's triangle

*Multiset

*Munkres' assignment algorithm **N***

Necklace (combinatorics)

*Necklace problem

*Negligible set

**Almost all

**Almost everywhere

**Null set

*Newton's identities **O***

Ordered partition of a set

*Orthogonal design

**Complex orthogonal design

**Quaternion orthogonal design **P***

Packing problem

**Bin packing problem

*Partition of a set

**Noncrossing partition

*Permanent

*Permutation

**Permutation matrix

**Permutations and combinations

**Josephus permutation

**Shuffling playing cards

*Pochhammer symbol

*Polyform s

**Polycube s

***Soma cube

**Polyiamond s

**Polyomino es

***Hexomino es

***Pentomino es

***Tetromino es

**Polysquare puzzle

*Projective plane

*Property B

*Prüfer sequence **Q***

q-analog

*q-binomial theorem—seeGaussian binomial

*q-derivative

*q-series

*q-theta function

*q-Vandermonde identity **R***

Rencontres numbers

*Rubik's cube

**

**Optimal solutions for Rubik's Cube

**Rubik's Revenge *

Schröder number

*Search algorithm

**Binary search

**Interpolation search

**Linear search

**Local search

**String searching algorithm

***Aho-Corasick algorithm

***Fuzzy string searching

***grep ,agrep ,wildcard character

***Knuth-Morris-Pratt algorithm

*Sequences with zero autocorrelation function

*Series-parallel networks problem

*Set cover problem

*Shuffling puzzle

*Small set (combinatorics)

*Sparse matrix ,Sparse array

*Sperner family

*Sperner's lemma

*Stable marriage problem

*Steiner system

*Stirling number

**Stirling transform

*String algorithm

*Straddling checkerboard

*Subsequence

**Longest common subsequence problem

***Optimal-substructure

*Subset sum problem

*Symmetric function s

*Szemerédi's theorem **T***

Thue-Morse sequence

*Tower of Hanoi

*Turán number

*Turing tarpit **U***

Urn problem s (probability)**V***

Vandermonde's identity **W***

Weighing matrices

*Weighted round robin

**Deficit round robin

*Wigner-d'Espagnat inequality **Y***

Young tableau **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**People***

Noga Alon

*George Andrews

*Eric Temple Bell

*Belá 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

*Solomon Golomb

*Ben Green

*Tim Gowers

*Gyula O. H. Katona

*Imré Leader

*Luke Pebody

*George Pólya

*Gian-Carlo Rota

*Cecil C. Rousseau

*Dick Schelp

*Vèra T. Sôs

*Joel Spencer

*Emanuel Sperner

*Richard P. Stanley

*Endre Szemerédi

*Terence Tao

*Jacques Touchard

*Bartel Leendert van der Waerden

*Herbert Wilf

*Doron Zeilberger **Journals*** 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 and 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

* 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 Lostharingien de Combinatoire

* SIAM Journal on Discrete Mathematics**Prizes***

Euler Medal **Publications***"

Geombinatorics "**ee 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

*combinatorial chemistry

*Wikimedia Foundation.
2010.*

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