MaximalExcedance on Permutation
The largest p(i) - i.
FindStat's title says drop size, i - p(i); its code takes p(i) - i. This follows the code.
Called as CombinatorialStat(x, "MaximalExcedance"). The head's page has its examples.
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FindStat St000141
The maximum drop size 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] | 1 |
[3,1,2] | 2 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000141 has the rest.