RowDescentsToColumnDescents

A standard tableau of the same shape whose column descents are the original's row descents.

FindStatMp00226via StandardTableau↗

RowDescentsToColumnDescents(StandardTableau)A standard tableau of the same shape whose column descents are the original's row descents.

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 Mp00226, a bijection. From the natural labelling of the shape, d and d + 1 are exchanged at each column descent d, the tableau following by the same exchange unless that keeps its descents.

Examples

Basic #

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

live ↗

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

About

Examples	1
Crosswalk	FindStat