TopLeftZeroSquareSize on AlternatingSignMatrix
The side of the largest square of zeros at the top left corner.
FindStat's St001981. The square of side z is all zeros exactly when z is below the largest of the row and column of every nonzero entry, so the side is the least such largest, less 1; an alternating sign matrix has a nonzero entry.
Called as CombinatorialStat(x, "TopLeftZeroSquareSize"). The head's page has its examples.
Live
Distribution
Over AlternatingSignMatrices at each size, tallied here in your browser; sizes past 6 are not offered.
FindStat St001981
The size of the largest square of zeros in the top left corner of an alternating sign matrix.
| Object | Value |
|---|---|
[[1]] | 0 |
[[0,1],[1,0]] | 1 |
[[1,0],[0,1]] | 0 |
[[0,0,1],[0,1,0],[1,0,0]] | 1 |
[[0,0,1],[1,0,0],[0,1,0]] | 1 |
[[0,1,0],[0,0,1],[1,0,0]] | 1 |
[[0,1,0],[1,0,0],[0,0,1]] | 1 |
[[1,0,0],[0,0,1],[0,1,0]] | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001981 has the rest.