SimionSchmidt

The left-to-right minima stay in place and the other positions take the remaining values, largest first: a 123-avoiding permutation.

FindStatMp00068via Permutation↗

SimionSchmidt(Permutation)The left-to-right minima stay in place and the other positions take the remaining values, largest first: a 123-avoiding permutation.

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 Mp00068, Sage's simion_schmidt(avoid=[1,2,3]). Idempotent; a bijection from the 132-avoiding permutations to the 123-avoiding ones.

Examples

Basic #

the identity $123$

live ↗

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

About

Examples	1
Crosswalk	FindStat