InverseFoataHan

The inverse of Foata and Han's transformation: the last letter is peeled off and the blocks of the rest are rotated back.

FindStatMp00194via SignedPermutation↗

InverseFoataHan(SignedPermutation)The inverse of Foata and Han's transformation: the last letter is peeled off and the blocks of the rest are rotated back.

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 Mp00194, sending the flag inversion number to the flag major index.

Examples

Basic #

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

live ↗

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

About

Examples	1
Crosswalk	FindStat