TableauPromotion

Promotion: replace the largest entry by a hole, slide it to the corner at the origin, and add one to every entry.

FindStatMp00155via StandardTableau↗

TableauPromotion(StandardTableau)Promotion: replace the largest entry by a hole, slide it to the corner at the origin, and add one to every entry.

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 Mp00155, the inverse of InverseTableauPromotion. The hole is walked through the rows entry by entry, as jeu de taquin does.

Examples

Basic #

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

live ↗

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

About

Examples	1
Crosswalk	FindStat