RookPlacementCount on SkewPartition
The placements of any number of non-attacking rooks on the cells of the shape.
FindStat's St001658. The empty placement counts. The table has 2^w entries for w columns, so a shape wider than about 20 columns is slow. The empty shape gives 1.
Called as CombinatorialStat(x, "RookPlacementCount"). The head's page has its examples.
Live
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 St001658
The total number of rook placements on a Ferrers board.
| Object | Value |
|---|---|
[[1],[]] | 2 |
[[2],[]] | 3 |
[[3],[]] | 4 |
[[4],[]] | 5 |
[[5],[]] | 6 |
[[6],[]] | 7 |
[[7],[]] | 8 |
[[1,1],[]] | 3 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001658 has the rest.