ShorterSideRookPlacementCount on IntegerPartition
The ways to place as many non-attacking rooks as the shorter side of the Ferrers board's bounding rectangle has cells, 0 when they do not fit.
FindStat's title calls this the leading coefficient of the rook polynomial, but its code takes the entry for the shorter side, which is 0 when no placement fills it; the name follows the code.
Called as CombinatorialStat(x, "ShorterSideRookPlacementCount"). 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 St000531
The leading coefficient of the rook polynomial of an integer partition.
| Object | Value |
|---|---|
[] | 1 |
[1] | 1 |
[2] | 2 |
[3] | 3 |
[4] | 4 |
[5] | 5 |
[6] | 6 |
[7] | 7 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000531 has the rest.