AlternatingSignMatrixPosetRank on AlternatingSignMatrix
Half the sum of (i - j)^2 a(i, j): the rank in the alternating sign matrix poset.
FindStat's St000076, which gives this formula for the rank (the sum of the monotone triangle's entries less n + 2 choose 3). The sum is never negative.
Called as CombinatorialStat(x, "AlternatingSignMatrixPosetRank"). The head's page has its examples.
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FindStat St000076
The rank of the alternating sign matrix in the alternating sign matrix poset.
| Object | Value |
|---|---|
[[1]] | 0 |
[[0,1],[1,0]] | 1 |
[[1,0],[0,1]] | 0 |
[[0,0,1],[0,1,0],[1,0,0]] | 4 |
[[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]] | 1 |
[[1,0,0],[0,0,1],[0,1,0]] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000076 has the rest.