BorderSkewStandardTableauCount on IntegerPartition
Standard tableaux of the skew shape that adds a cell to every column of the diagram: the size factorial over the factorials of the cells added to each row (the size less the largest part, then the gaps between consecutive parts).
Called as CombinatorialStat(x, "BorderSkewStandardTableauCount"). 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.
FindStat St001387
Number of standard Young tableaux of the skew shape tracing the border of the given 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/St001387 has the rest.