MaximalRookPlacementCount on SkewPartition
The ways to place as many non-attacking rooks as possible on the cells of the shape.
FindStat's St001660, the last nonzero rook number of the shape, from the table of RookPlacementCount. The empty shape gives 1.
Called as CombinatorialStat(x, "MaximalRookPlacementCount"). The head's page has its examples.
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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 St001660
The number of ways to place as many non-attacking rooks as possible on a skew Ferrers board.
| Object | Value |
|---|---|
[[1],[]] | 1 |
[[2],[]] | 2 |
[[3],[]] | 3 |
[[4],[]] | 4 |
[[5],[]] | 5 |
[[6],[]] | 6 |
[[7],[]] | 7 |
[[1,1],[]] | 2 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001660 has the rest.