Combinatorics 1-24
22 entries in the Combinatorics compendium.
Algebraic combinatoricsArea of mathematics combining abstract algebra and combinatorics.Binomial theoremDescribes the expansion of powers of a binomial.CombinatoricsMathematics of counting, arrangement, and optimization in finite systems.BijectionA function pairing each element of two sets exactly once.Bijection, injection and surjectionClasses of functions defined by mapping properties.Binomial (polynomial)A polynomial consisting of exactly two monomial terms.Bell numberBell numbers count set partitions and have ancient roots.Binomial coefficientPositive integers that appear as coefficients in the binomial theorem.Binomial seriesGeneralized binomial formula for complex exponents.Catalan numberSequence of natural numbers in counting problems.CombinationA selection of items from a set where order does not matter.Combinatorial principlesFoundational rules for counting and proving in combinatorics.Double counting (proof technique)A combinatorial proof technique equating two expressions by counting one set.Pigeonhole principleIf n items go into m boxes and n > m, one box holds more.Ramsey theoryBranch of combinatorics on guaranteed order in large structures.PermutationA bijection rearranging a set's elements into a new order.Partial permutationBijection between two equal-sized subsets of a finite set.Pascal's triangleTriangular array of binomial coefficients used in combinatorics and algebra.Stirling numberNumbers describing coefficients in polynomial expansions and partitions.Stirling numbers of the first kindNumbers counting permutations by cycles and factorial expansions.Stirling numbers of the second kindNumbers counting partitions of a set into nonempty subsets.Twelvefold wayClassification of 12 enumerative problems in combinatorics.
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