UpperInteractions on DyckPath
Over each valley, the shorter of the down run before it and the up run after it, summed: the factors of k down steps then k up steps.
Over a valley, the shorter of the down run before it and the up run after it.
Called as CombinatorialStat(x, "UpperInteractions"). 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 St000331
The number of upper interactions of a Dyck path.
| Object | Value |
|---|---|
[1,0] | 0 |
[1,0,1,0] | 1 |
[1,1,0,0] | 0 |
[1,0,1,0,1,0] | 2 |
[1,0,1,1,0,0] | 1 |
[1,1,0,0,1,0] | 1 |
[1,1,0,1,0,0] | 1 |
[1,1,1,0,0,0] | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000331 has the rest.