InversionIndex on Permutation
The sum of the larger entry p(i) over the inversions i < j.
Called as CombinatorialStat(x, "InversionIndex"). 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 St000616
The inversion index of a permutation.
| Object | Value |
|---|---|
[1] | 0 |
[1,2] | 0 |
[2,1] | 2 |
[1,2,3] | 0 |
[1,3,2] | 3 |
[2,1,3] | 2 |
[2,3,1] | 5 |
[3,1,2] | 6 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000616 has the rest.