ReadingTableau

The recording tableau of the row reading word of the shape filled row by row.

FindStatMp00045via IntegerPartition↗

ReadingTableau(IntegerPartition)The recording tableau of the row reading word of the shape filled row by row.

Typed signatures

Type	Package	Applies
(integer_partition) -> standard_tableau	combinatorics	always

Domain: Combinatorial maps

Details

• Takes a IntegerPartition and returns a StandardTableau — a typed map, so a wrong carrier is a type error rather than a wrong answer.
• Defined as a COMPOSITION, applied right to left: RskRecording after ReadingWord after InitialTableau. Each step goes through its own declared head, so every intermediate value is a properly constructed carrier.
• FindStat's Mp00045. Injective. The RSK insertion tableau of that word is the filled shape again, so this is the other half of its pair.

Examples

Basic #

the partition $4 + 2 + 1$

live ↗

In$\mathrm{ReadingTableau}({\operatorname{IntegerPartition}}([4, 2, 1]))$Out${\operatorname{StandardTableau}}([[1, 3, 6, 7], [2, 5], [4]])$

About

Examples	1
Crosswalk	FindStat

See also: RskRecording, ReadingWord, InitialTableau