Category:Combinatorics

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Combinatorics is a branch of mathematics that studies finite collections of objects that satisfy specified criteria, and is in particular concerned with "counting" the objects in those collections (enumerative combinatorics) and with deciding whether certain "optimal" objects exist (extremal combinatorics). One of the most prominent combinatorialists of recent times was Gian-Carlo Rota, who helped formalize the subject beginning in the 1960s. The prolific problem-solver Paul Erdős worked mainly on extremal questions. The study of how to count objects is sometimes thought of separately as the field of enumeration.

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Subcategories

There are 11 subcategories to this category.

C Combinatorial game theory Combinatorists D Discrete geometry

D cont. Discrete mathematics G Graph theory I Incidence geometry Integer sequences

Q Q-analogs R Ramsey theory S Set families Special functions

Articles in category "Combinatorics"

There are 116 articles in this category.

A Algebraic enumeration All-pairs testing Alternating sign matrix Analytic combinatorics Antichain B Bell polynomials Bertrand's ballot theorem Bijective proof Binomial coefficient Binomial theorem Binomial type Block design Bruck-Chowla-Ryser theorem C Catalan number Combinadic Combination Combinatorial class Combinatorial enumeration Combinatorial principles Combinatorial proof Combinatorial species Combinatorics Costas array Covering problem Cubing the cube Cycle decomposition Cyclic permutation D De Bruijn sequence Derangement Dickson's lemma Dinitz conjecture Dividing a circle into areas Double counting E Eight queens puzzle Enumeration Even and odd permutations Exponential formula F Factoradic

F cont. Factorial Faà di Bruno's formula Fibonacci word Floyd's cycle-finding algorithm Formal power series G Garden of Eden pattern Gaussian binomial Generating function Graeco-Latin square Gray code Greedoid H Hypergeometric function identities Hypergeometric series Hypergraph I Incidence algebra Incidence structure Inclusion-exclusion principle K Kakeya needle problem Kruskal-Katona theorem L Lagrange reversion theorem Lah number Latin square Laver table Levi-Civita symbol List of combinatorics topics List of factorial and binomial topics List of partition topics List of publications in mathematics Littlewood-Offord problem Longest-common subsequence problem Look and Say sequence Lubell-Yamamoto-Meshalkin inequality M Marriage theorem Matroid Method of distinguished element Moreau's necklace-counting function Multi-index notation Multinomial theorem Möbius inversion formula

O Ordered partition of a set P Partition function (number theory) Partition of a set Pascal's pyramid Pascal's triangle Percolation theory Permutation Permutations and combinations Pigeonhole principle Pochhammer symbol Probabilistic method Prüfer sequence R Random permutation Robinson-Schensted algorithm Rule of product Rule of sum S Sieve theory Sim (Pencil Game) Small set Sparse matrix Sperner's lemma Stable marriage problem Stanley's reciprocity theorem Stirling number Stirling transform Sturmian word Subfactorial Sum-free sequence Sylvester-Gallai theorem Symbolic combinatorics Symmetric function Szemerédi's theorem Szemerédi-Trotter theorem T Thue-Morse sequence Transversal Trinomial expansion U Umbral calculus V Vandermonde's identity W Weight function

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