TotalDisplacement on Permutation
The sum of |p(i) - i|.
Called as CombinatorialStat(x, "TotalDisplacement"). 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.
FindStat St000830
The total displacement of a permutation.
| Object | Value |
|---|---|
[1,2] | 0 |
[2,1] | 2 |
[1,2,3] | 0 |
[1,3,2] | 2 |
[2,1,3] | 2 |
[2,3,1] | 4 |
[3,1,2] | 4 |
[3,2,1] | 4 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000830 has the rest.