Foata

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

FindStatMp00067via Permutation↗

Foata(Permutation)

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