ValleyPositionSum on DyckPath
The sum of the positions of the valleys: a down step followed by an up step.
FindStat St000027, "the major index of a Dyck path"; the repo's MajorIndex on a Dyck path sums the peaks' positions instead.
Called as CombinatorialStat(x, "ValleyPositionSum"). The head's page has its examples.
Live
Distribution
Over DyckPaths at each size, tallied here in your browser; sizes past 10 are not offered.
FindStat St000027
The major index of a Dyck path.
| Object | Value |
|---|---|
[] | 0 |
[1,0] | 0 |
[1,0,1,0] | 2 |
[1,1,0,0] | 0 |
[1,0,1,0,1,0] | 6 |
[1,0,1,1,0,0] | 2 |
[1,1,0,0,1,0] | 4 |
[1,1,0,1,0,0] | 3 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000027 has the rest.