DistinctDiagonalSums on Permutation

The number of distinct sums along the diagonals of the permutation matrix.

On Permutation

The sum along the diagonal k counts the i with p(i) - i = k, empty diagonals included.

Called as CombinatorialStat(x, "DistinctDiagonalSums"). The head's page has its examples.

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Distribution

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Sizes 1 to

FindStat St000891

The number of distinct diagonal sums of a permutation matrix.

Object	Value
[]	0
[1]	1
[1,2]	2
[2,1]	2
[1,2,3]	2
[1,3,2]	2
[2,1,3]	2
[2,3,1]	3

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000891 has the rest.