DescentWordFiberSize on Permutation

The permutations of the same size with the same descents as p.

On Permutation

Counted by the rank of the last entry: a descent keeps the partial sums from the right, an ascent from the left.

Called as CombinatorialStat(x, "DescentWordFiberSize"). 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 St000530

The number of permutations with the same descent word as the given permutation.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000530 has the rest.