MatrixInversionNumber on AlternatingSignMatrix
The sum of a(i, j) a(k, l) over the pairs of entries with i > k and j < l.
FindStat's St000067. On a permutation matrix it is the number of inversions.
Called as CombinatorialStat(x, "MatrixInversionNumber"). 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 St000067
The inversion number of the 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/St000067 has the rest.