Enumerative combinatorics

recursive integer sequence

mathematical chess problem of placing eight chess queens on an 8×8 chessboard so that no two queens threaten each other

counting technique in combinatorics

generalization of a polynomial, where the number of terms is allowed to be infinite, defined algebraically without consideration of convergence (so that e.g. evaluation is not always defined)

number of patterns of non-intersecting chords with a given number of endpoints on a circle

mathematical sequence

product of all the integers from 1 up to the integral input of the function that have the same parity as this input

relation between pairs of arithmetic functions

thumb|The distribution of permutations in a 3-symbol superpermutation In combinatorial mathematics, a superpermutation on n symbols is a string that contains each permutation of n symbols as a substring. While trivial superpermutations can simply be made up of every permutation concatenated together, superpermutations can also be shorter (except for the trivial case of n = 1) because overlap is allowed. For instance, in the case of n = 2, the superpermutation 1221 contains all possible permutations (12 and 21), but the shorter string 121 also contains both permutations.

An enumeration is a complete, ordered listing of all the items in a collection. The term is commonly used in mathematics and computer science to refer to a listing of all of the elements of a set. The precise requirements for an enumeration (for example, whether the set must be finite, or whether the list is allowed to contain repetitions) depend on the discipline of study and the context of a given problem.

circular sequence of symbols that contains each possible length-k contiguous subsequence exactly once

number of permutations of the numbers from 1 to n in which m elements are greater than the previous element

area of combinatorics that deals with the number of ways that certain patterns can be formed

theorem that, in an election where candidate A receives 𝑝 votes and candidate B receives 𝑞 votes (𝑝>𝑞), the probability that A will be strictly ahead of B throughout the count is (𝑝−𝑞)/(𝑝+𝑞)

mathematical integer sequence

theorem

theorem

triangular array of polynomials in combinatorial mathematics

proof technique in combinatorics that finds a bijection between the things to be counted and some easily countable things

technique for proving that two expressions are equal by showing that they both count the size of the same set

an equivalence class of n-character strings over an alphabet of size k, taking all rotations as equivalent

combinatorial sequence of numbers

Polynomial in combinatorial mathematics

mathematical model also called the Razumov–Stroganov conjecture

class of combinatorial enumeration problems

type of permutation studied in combinatorics

number in combinatorics

generating polynomial of the number of ways to place k non-attacking rooks on a m×n chessboard

endofunctor on the category of finite sets and bijections, which can be used to analyse discrete structures in terms of generating functions

On finite sums of products of three binomial coefficients, and a hypergeometric sum

Concept in combinatorial mathematics

mathematical constant used in combinatorics

technique for counting combinatorial objects, using the internal structure of the objects to derive formulas for their generating functions