MainDiagonalSum on AlternatingSignMatrix
The sum of the entries on the main diagonal, its trace.
FindStat's St000894. The entries are -1, 0 and 1, so the trace is the number of 1s on the diagonal less the number of -1s.
Called as CombinatorialStat(x, "MainDiagonalSum"). 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 St000894
The trace of an alternating sign matrix.
| Object | Value |
|---|---|
[[0,1],[1,0]] | 0 |
[[1,0],[0,1]] | 2 |
[[0,0,1],[0,1,0],[1,0,0]] | 1 |
[[0,0,1],[1,0,0],[0,1,0]] | 0 |
[[0,1,0],[0,0,1],[1,0,0]] | 0 |
[[0,1,0],[1,0,0],[0,0,1]] | 1 |
[[1,0,0],[0,0,1],[0,1,0]] | 1 |
[[1,0,0],[0,1,0],[0,0,1]] | 3 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000894 has the rest.