Nestings on Permutation
Pairs i, j with j < i < p(i) < p(j) or p(j) < p(i) <= i < j.
Nestings of the arcs of the permutation diagram.
Called as CombinatorialStat(x, "Nestings"). 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 St000223
The number of nestings in the 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] | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000223 has the rest.