FoataHan

Foata and Han's fundamental transformation: each letter in turn is put on the end of the image so far, which is cut into blocks and rotated.

FindStatMp00190via SignedPermutation↗

FoataHan(SignedPermutation)Foata and Han's fundamental transformation: each letter in turn is put on the end of the image so far, which is cut into blocks and rotated.

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 Mp00190, a bijection that sends the flag major index to the flag inversion number. Inverse: InverseFoataHan.

Examples

Basic #

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

live ↗

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

About

Examples	1
Crosswalk	FindStat