PermutationTreeHeight on Permutation

The height of the rooted tree from inserting the entries one by one, the most entries on the stack of ancestors.

On Permutation

Called as CombinatorialStat(x, "PermutationTreeHeight"). 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 St000308

The height of the tree associated to a permutation.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000308 has the rest.