# 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](/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+) -> 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 where S: string) & ((collection, integer) -> 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 where S: string) & ((collection, integer?) -> 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) -> 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.