Foata

Foata's fundamental bijection: cycles rotated to their max, ordered by increasing max, parentheses erased.

FindStatMp00087via Permutation↗

Foata(Permutation)Foata's fundamental bijection: cycles rotated to their max, ordered by increasing max, parentheses erased.

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.
• The first fundamental transformation — it sends a permutation with k cycles to one with k left-to-right maxima. (The catalog's title also names maj → inv, which is the SECOND fundamental transformation's property; this map is the first.)

Examples

Basic #

the one-line word $231$

live ↗

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

About

Examples	1
Crosswalk	FindStat