StandardTableauCount on IntegerPartition
The number of standard Young tableaux of the shape: the size factorial over the hook product.
Defined by the hook-length formula; PlancherelCount is its square.
Called as CombinatorialStat(x, "StandardTableauCount"). The head's page has its examples.
Live
Distribution
Over IntegerPartitions at each size, tallied here in your browser; sizes past 30 are not offered.
Also on
The same name on other carriers, each its own implementation: SkewPartition.
FindStat St000003
The number of standard Young tableaux of the partition.
The number of [[/StandardTableaux|standard Young tableaux]] of the partition.
| Object | Value |
|---|---|
[] | 1 |
[1] | 1 |
[2] | 1 |
[3] | 1 |
[4] | 1 |
[5] | 1 |
[6] | 1 |
[7] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000003 has the rest.