MaximalDiagonalOccupancy on Permutation

The most entries on one diagonal of the permutation matrix: the largest number of i sharing a p(i) - i.

On Permutation

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

Live

Distribution

Over SymmetricGroup at each size, tallied here in your browser; sizes past 8 are not offered.

Sizes 1 to

FindStat St000887

The maximal number of nonzero entries on a diagonal of a permutation matrix.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000887 has the rest.