MatrixPermanent on AlternatingSignMatrix
The permanent: the sum over the permutations s of the product of a(i, s(i)).
FindStat's St001260. Ryser's formula: (-1)^n times the sum over the sets S of columns of (-1)^|S| times the product over the rows of the row's sum over S. The sets are the numbers 0 .. 2^n - 1 read in binary.
Called as CombinatorialStat(x, "MatrixPermanent"). 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 St001260
The permanent of an alternating sign matrix.
| Object | Value |
|---|---|
[[1]] | 1 |
[[0,1],[1,0]] | 1 |
[[1,0],[0,1]] | 1 |
[[0,0,1],[0,1,0],[1,0,0]] | 1 |
[[0,0,1],[1,0,0],[0,1,0]] | 1 |
[[0,1,0],[0,0,1],[1,0,0]] | 1 |
[[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/St001260 has the rest.