SkewHookPositionSum on DyckPath
The sum of the skew hook positions: after two up steps and a down step, the down step's rank among the down steps; after two down steps and an up step, the rank of the second down step.
Called as CombinatorialStat(x, "SkewHookPositionSum"). The head's page has its examples.
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FindStat St000946
The sum of the skew hook positions in a Dyck path.
| Object | Value |
|---|---|
[1,0,1,0] | 0 |
[1,1,0,0] | 1 |
[1,0,1,0,1,0] | 0 |
[1,0,1,1,0,0] | 2 |
[1,1,0,0,1,0] | 3 |
[1,1,0,1,0,0] | 1 |
[1,1,1,0,0,0] | 1 |
[1,0,1,0,1,0,1,0] | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000946 has the rest.