Inverse

The inverse permutation: position of each value.

Inverse(Permutation)The inverse permutation: position of each value.

Typed signatures

Type	Package	Applies
`(matrix) -> matrix`	`compute-engine`	always
`((permutation) -> permutation) & ((signed_permutation) -> signed_permutation)`	`combinatorics`replaces `modular`	on permutation, signed_permutation
`(expression<ModularMatrix> \| matrix \| string) -> expression<ModularMatrix> \| matrix`	`modular`replaces `compute-engine`	always

Domain: Combinatorial maps

Details

Takes a Permutation and returns a Permutation — a typed map, so a wrong carrier is a type error rather than a wrong answer.
Also takes a SignedPermutation, returning a SignedPermutation: The inverse signed permutation: ±j goes to the position of j, signed as the entry there.
FindStat's Mp00162.

Examples

Basic #

the one-line word $231$

{\operatorname{Permutation}}([2, 3, 1])^{-1}

Out

{\operatorname{Permutation}}([3, 1, 2])

the signed permutation $2\,\bar 3\,1$

{\operatorname{SignedPermutation}}([2, -3, 1])^{-1}

Out

{\operatorname{SignedPermutation}}([3, 1, -2])

About

Examples	2
Crosswalk	Wikipedia ×2 MathWorld Wikidata Encyclopedia of Mathematics nLab Britannica FindStat ×2 Wolfram Language

mappedsagepackages/oracle/src/mappings.ts

mappedsympypackages/oracle/src/mappings.ts

The permutation inverse (Permutation.__invert__), 1-based in and out; not a matrix inverse.