PositiveMatrixInversionNumber on AlternatingSignMatrix
The inversion number less the number of entries equal to -1.
FindStat's St000332.
Called as CombinatorialStat(x, "PositiveMatrixInversionNumber"). 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 St000332
The positive inversions 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]] | 3 |
[[0,0,1],[1,0,0],[0,1,0]] | 2 |
[[0,1,0],[0,0,1],[1,0,0]] | 2 |
[[0,1,0],[1,0,0],[0,0,1]] | 1 |
[[1,0,0],[0,0,1],[0,1,0]] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000332 has the rest.