This page gathers the 27 dictionary entries belonging to the domain “Combinatorics”, as labelled by Wiktionary. Each word leads to its full entry: definitions, etymology, pronunciation, examples.
- algebraic combinatorics noun A branch of mathematics in which techniques from abstract algebra are applied to problems in combinatorics, and vice versa.
- back substitution noun A method of solving recurrence relations.
- Bell number noun Any member of a sequence of numbers that count the possible partitions of a set, such that the nth number Bₙ is the number of different…
- Bell polynomial noun Any member of a certain class of polynomials used in the study of set partitions, and related to Stirling numbers and Bell numbers.
- binomial coefficient noun a coefficient of any of the terms in the expansion of the binomial (x+y)ⁿ, defined by n choose k=(n!)/(k!(n-k)!), read as "n choose k"
- cover noun A collection (or family) of subsets of a given set, whose union contains every element of said original set.
- de Bruijn torus noun An array of symbols from an alphabet (often just 0 and 1) that contains every m-by-n matrix exactly once.
- derangement noun A permutation of a set such that no element is in its previous position.
- difference set noun A subset of a group such that any element of the group can be expressed as the difference (or the quotient) of two elements in such subset.
- double factorial noun For an odd integer, the result of multiplying all the odd integers from 1 to the given number; or for an even integer, the result of…
- Dyck word noun A string consisting of n X's and n Y's such that no initial segment of the string has more Y's than X's.
- exact cover noun Given a collection S of subsets of a set X, a subcollection S^* of S such that each element of X is contained in exactly one subset in S^*.
- excedance noun A position in a permutation occupied by a value greater than the position number.
- factorial noun The result of multiplying a given number of consecutive integers from 1 to the given number. In equations, it is symbolized by an…
- graphoid noun A matroid that has two collections of nonempty subsets called circuits and cocircuits such that the intersection of any circuit and…
- Helly dimension noun A value associated with a metric space, being one less than the Helly number of the family of metric balls in that space.
- Helly family noun A family of order k of sets, such that any minimal subfamily with an empty intersection has k or fewer sets in it.
- jeu de taquin slide noun A transformation that moves around the numbers in a tableau according to the jeu de taquin construction, used to determine whether tableaux…
- matroid noun A structure that captures the essence of a notion of "independence" that generalizes linear independence in vector spaces and acyclicality…
- Möbius function noun A function from the natural numbers to the set {−1, 0, 1} which maps perfect squares to 0, prime numbers to −1, and is multiplicative.
- Narayana number noun Any of the triangular array of natural numbers defined by N(n, k), n = 1, 2, 3 ..., 1 ≤ k ≤ n, occurring in various counting problems.
- permanent noun Given an n×n matrix a_ij,, the sum over all permutations π, of ∏ᵢ₌₁ⁿa_iπ(i).
- permutation noun An ordering of a finite set of distinct elements.
- Poissonization noun Analysis of a multivariate combinatorial distribution by turning interdependent variables into independent Poisson distributions.
- Ramsey number noun Any one of a certain set of numbers which are guaranteed to exist by Ramsey's theorem; a positive integer which is a certain function of…
- rook polynomial noun A generating polynomial of the number of ways to place non-attacking rooks on a generalized form of chessboard.
- Sperner family noun A family F of subsets of a finite set E in which none of the sets contains another; or, equivalently, an antichain in the inclusion lattice…