MaximalDiagonalSum on AlternatingSignMatrix
The largest sum of the entries along a diagonal.
The diagonals are the cells (i, j) with i - j fixed. A sum is floored at 0, which no sum of a corner cell falls below, so the largest is unchanged.
Called as CombinatorialStat(x, "MaximalDiagonalSum"). 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 St000888
The maximal sum of entries on a diagonal of an alternating sign matrix.
| Object | Value |
|---|---|
[[0,1],[1,0]] | 1 |
[[1,0],[0,1]] | 2 |
[[0,0,1],[0,1,0],[1,0,0]] | 1 |
[[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 |
[[1,0,0],[0,1,0],[0,0,1]] | 3 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000888 has the rest.