InverseFoata

The permutation whose cycles are the stretches of the word between successive left-to-right maxima, each read as a cycle.

FindStatMp00086via Permutation↗

InverseFoata(Permutation)The permutation whose cycles are the stretches of the word between successive left-to-right maxima, each read as a cycle.

Typed signatures

Type	Package	Applies
(permutation) -> permutation	combinatorics	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.
• FindStat's Mp00086, the inverse of Foata: a word's left-to-right maxima open its cycles.

Examples

Basic #

the one-line word $231$

live ↗

In$\mathrm{InverseFoata}({\operatorname{Permutation}}([2, 3, 1]))$Out${\operatorname{Permutation}}([3, 2, 1])$

About

Examples	1
Crosswalk	FindStat