Permutations

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

WikipediaPermutationMathWorldPermutationWikidataQ161519Encyclopedia of MathematicsPermutationnLabpermutationBritannicatopic/permutationOEISA000142Wolfram LanguageQFactorialSageMathPermutations(n)SymPygenerate_bellmathlib4Equiv.Perm (Fin n)MATLABpermsRosetta CodePermutations

Permutations(xs, k)The permutations of length k (default full length) of a collection, as compute-engine declares it.

Permutations(n)The permutations of

\{1, \ldots, n\}

as one-line words: the collection SymmetricGroup(n).

Typed signatures

Type	Package	Applies
`((S, integer?) -> list<string> where S: string) & ((collection, integer?) -> list<list>)`	`compute-engine`	always
`((S, integer?) -> list<string> where S: string) & ((collection, integer?) -> list<list>) & ((integer<0..>) -> indexed_collection<permutation>)`	`combinatorics`replaces `compute-engine`	always

Domain: Compute engine

Examples

Basic #

Permutations(n) is the collection of permutations of $\{1, \ldots, n\}$ , the same as SymmetricGroup(n)

\mathrm{Count}(\mathrm{Permutations}(4))

Out

24

About

Examples	1
Crosswalk	Wikipedia MathWorld Wikidata Encyclopedia of Mathematics nLab Britannica OEIS Wolfram Language SageMath SymPy mathlib4 MATLAB Rosetta Code