TwoByTwoSquareCount on SkewPartition
The cells of the shape whose neighbors to the right, below and below to the right are also in it.
FindStat's St001596. A cell (i, j) with the cell (i + 1, j + 1) also in the shape is the top left of a square, so row i counts the columns from μᵢ to λᵢ₊₁ - 2. The empty shape gives 0.
Called as CombinatorialStat(x, "TwoByTwoSquareCount"). 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.
FindStat St001596
The number of two-by-two squares inside a skew partition.
| Object | Value |
|---|---|
[[1],[]] | 0 |
[[2],[]] | 0 |
[[3],[]] | 0 |
[[4],[]] | 0 |
[[5],[]] | 0 |
[[6],[]] | 0 |
[[7],[]] | 0 |
[[1,1],[]] | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001596 has the rest.