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.

Subcategories

There are 9 subcategories to this category.

Combinatorial game theory Combinatorists D Discrete geometry

G Graph theory I Incidence geometry Integer sequences R Ramsey theory

S Set families Special functions

Articles in category "Combinatorics"

There are 96 articles in this category.

Algebraic enumeration Alternating sign matrix Analytic combinatorics Antichain B Bertrand's ballot theorem Binomial coefficient Binomial type Block design Bruck-Chowla-Ryser theorem C Catalan number Combinadic Combination Combinatorial class Combinatorial enumeration Combinatorial principles Combinatorial proof Combinatorial species Combinatorics 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 F Factoradic

F cont. Factorial 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 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 List of combinatorics topics List of factorial and binomial topics List of partition topics Longest-common subsequence problem Look and Say sequence Lubell-Yamamoto-Meshalkin inequality M Matroid Matroid embedding Method of distinguished element Moreau's necklace-counting function Multinomial theorem Möbius inversion formula

P Partition function (number theory) Partition of a set Pascal's pyramid Pascal's triangle Percolation theory Permutation Permutations and combinations Pigeonhole principle Probabilistic method Prüfer sequence Q Q-series R Random permutation Rule of product Rule of sum S Sieve theory Sim (Pencil Game) Small set Sparse matrix Sperner's lemma Stanley's reciprocity theorem Stirling number Sturmian word Subfactorial Sylvester-Gallai theorem Symbolic combinatorics Symmetric function Szemerédi's theorem Szemerédi-Trotter theorem T Thue-Morse sequence V Vandermonde's identity W Weight function