DistinctDiagonalSumCount on AlternatingSignMatrix
The number of distinct sums of the entries along a diagonal.
FindStat's St000893. A middle diagonal can sum below 0, so each sum is raised by the side before it is floored; raising every sum alike leaves the number of distinct ones.
Called as CombinatorialStat(x, "DistinctDiagonalSumCount"). The head's page has its examples.
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Distribution
Over AlternatingSignMatrices at each size, tallied here in your browser; sizes past 6 are not offered.
FindStat St000893
The number of distinct diagonal sums of an alternating sign matrix.
| Object | Value |
|---|---|
[[0,1],[1,0]] | 2 |
[[1,0],[0,1]] | 2 |
[[0,0,1],[0,1,0],[1,0,0]] | 2 |
[[0,0,1],[1,0,0],[0,1,0]] | 3 |
[[0,1,0],[0,0,1],[1,0,0]] | 3 |
[[0,1,0],[1,0,0],[0,0,1]] | 2 |
[[1,0,0],[0,0,1],[0,1,0]] | 2 |
[[1,0,0],[0,1,0],[0,0,1]] | 2 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000893 has the rest.