AssociatedStandardTableau

The standard tableau whose j-th column holds the j-th smallest elements of the blocks, in increasing order.

FindStatMp00258via SetPartition↗

AssociatedStandardTableau(SetPartition)The standard tableau whose j-th column holds the j-th smallest elements of the blocks, in increasing order.

Typed signatures

Type	Package	Applies
(set_partition) -> standard_tableau	combinatorics	always

Domain: Combinatorial maps

Details

• Takes a SetPartition and returns a StandardTableau — a typed map, so a wrong carrier is a type error rather than a wrong answer.
• FindStat's Mp00258. Not injective.

Examples

Basic #

the set partition $\{1,3\} \mid \{2\} \mid \{4\}$

live ↗

In$\mathrm{AssociatedStandardTableau}({\operatorname{SetPartition}}([[1, 3], [2], [4]]))$Out${\operatorname{StandardTableau}}([[1, 3], [2], [4]])$

About

Examples	1
Crosswalk	FindStat