DemazureProductWithInverse

The Demazure product π⁻¹ ⋆ π in the hyperoctahedral group.

FindStatMp00260via SignedPermutation↗

DemazureProductWithInverse(SignedPermutation)The Demazure product π⁻¹ ⋆ π in the hyperoctahedral group.

Typed signatures

Type	Package	Applies
(signed_permutation) -> signed_permutation	combinatorics	always

Domain: Combinatorial maps

Details

• Takes a SignedPermutation and returns a SignedPermutation — a typed map, so a wrong carrier is a type error rather than a wrong answer.
• FindStat's Mp00260: π⁻¹ ⋆ π, the inverse on the left. Not injective: it is a surjection onto the involutions. The group is generated by the adjacent transpositions and the sign change of the largest value.

Examples

Basic #

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

live ↗

In$\mathrm{DemazureProductWithInverse}({\operatorname{SignedPermutation}}([2, -3, 1]))$Out${\operatorname{SignedPermutation}}([-3, 2, -1])$

About

Examples	1
Crosswalk	FindStat