ShiftedStandardTableauCount on IntegerPartition
Standard tableaux of the shifted shape: the multinomial of the parts times, over pairs of parts, the difference over the sum. 0 when two parts are equal.
Called as CombinatorialStat(x, "ShiftedStandardTableauCount"). The head's page has its examples.
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Distribution
Over IntegerPartitions at each size, tallied here in your browser; sizes past 30 are not offered.
FindStat St001593
This is the number of standard Young tableaux of the given shifted shape.
| Object | Value |
|---|---|
[1] | 1 |
[2] | 1 |
[3] | 1 |
[4] | 1 |
[5] | 1 |
[6] | 1 |
[7] | 1 |
[8] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001593 has the rest.