Evacuation

Schützenberger's evacuation (involution): remove the entry 1, slide the rest in, and give the cell that empties the largest label, until nothing is left.

FindStatMp00085via StandardTableau↗

Evacuation(StandardTableau)Schützenberger's evacuation (involution): remove the entry 1, slide the rest in, and give the cell that empties the largest label, until nothing is left.

Typed signatures

Type	Package	Applies
(standard_tableau) -> standard_tableau	combinatorics	always

Domain: Combinatorial maps

Details

• Takes a StandardTableau and returns a StandardTableau — a typed map, so a wrong carrier is a type error rather than a wrong answer.
• FindStat's Mp00085. Computed as the insertion tableau of the reading word reversed and complemented; the same shape, and an involution.

Examples

Basic #

the standard tableau with rows $13$ and $2$

live ↗

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

About

Examples	1
Crosswalk	FindStat