StandardTableauCount on SkewPartition
The standard Young tableaux of the shape: the ways to fill its cells with 1 .. n, rising along rows and down columns.
FindStat's St001595. Counted over the order ideals of the shape, a filling being a walk that adds one cell at a time; the table has one entry for each, up to 2^n, so a shape of 20 cells in as many rows is slow. The empty shape gives 1.
Called as CombinatorialStat(x, "StandardTableauCount"). The head's page has its examples.
Live
Distribution
Over SkewPartitions at each size, tallied here in your browser; sizes past 6 are not offered.
Also on
The same name on other carriers, each its own implementation: IntegerPartition.
FindStat St001595
The number of standard Young tableaux of the skew partition.
| Object | Value |
|---|---|
[[1],[]] | 1 |
[[2],[]] | 1 |
[[3],[]] | 1 |
[[4],[]] | 1 |
[[5],[]] | 1 |
[[6],[]] | 1 |
[[7],[]] | 1 |
[[1,1],[]] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001595 has the rest.