Crossings on Permutation
Pairs i, j with i < j <= p(i) < p(j) or p(i) < p(j) < i < j.
Crossings of the arcs of the permutation diagram (Corteel).
Called as CombinatorialStat(x, "Crossings"). 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.
Also on
The same name on other carriers, each its own implementation: SetPartition.
FindStat St000039
The number of crossings of a permutation.
| Object | Value |
|---|---|
[] | 0 |
[1] | 0 |
[1,2] | 0 |
[2,1] | 0 |
[1,2,3] | 0 |
[1,3,2] | 0 |
[2,1,3] | 0 |
[2,3,1] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000039 has the rest.