Depth on Permutation

Half the total displacement, (1/2) * sum |p(i) - i|.

On Permutation

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

Live

FindStat St000029

The depth of a permutation.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000029 has the rest.