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Combinatorics

The 11 definitions of the combinatorics library, each with its Epsil spelling, its MathJSON name, its signature and its full description.

Each definition is listed under its Epsil spelling (the MathJSON name when it has none), with its signature in the engine's type syntax. The Standard Library page is the one-page index of every category.

Definitions​

bellNumber​

MathJSON BellNumber · (integer) -> integer

Compute the Bell number B(n), the number of partitions of a set of n elements.

binomial​

MathJSON Binomial · (complex | infinity, complex | infinity) -> number

Compute the binomial coefficient C(n, k) = n! / (k! (n-k)!). Agrees with Choose for all defined values.

cartesianProduct​

MathJSON CartesianProduct · (set<any>+) -> set

Return the Cartesian product of input sets.

choose​

MathJSON Choose · (n: complex | infinity, m: complex | infinity) -> number

Binomial coefficient: number of ways to choose k items from n. Agrees with Binomial for all defined values.

combinations​

MathJSON Combinations · ((S, integer) -> list<string> where S: string) & ((collection, integer) -> list<list>)

Return all k-element combinations of a collection.

fibonacci​

MathJSON Fibonacci · (integer) -> integer

Compute the nth Fibonacci number.

multinomial​

MathJSON Multinomial · (integer+) -> integer

Compute the multinomial coefficient for multiple integers.

permutations​

MathJSON Permutations · ((S, integer?) -> list<string> where S: string) & ((collection, integer?) -> list<list>)

Return all permutations of length k (default full length) of a collection.

pochhammer​

MathJSON Pochhammer · (complex | infinity, complex | infinity) -> number

Rising factorial (Pochhammer symbol) (a)_k = a(a+1)…(a+k-1).

powerSet​

MathJSON PowerSet · (set<any>) -> set

Return the power set of a set (set of all subsets).

subfactorial​

MathJSON Subfactorial · (integer) -> integer

Compute the number of derangements (subfactorial) of n items.