DyckPathsAboveBouncePathCount on IntegerComposition
Dyck paths of semilength n that stay weakly above the bounce path of the composition: their area sequences are at least 0 .. c_1 - 1, 0 .. c_2 - 1, ....
FindStat titles it the parabolic noncrossing partitions indexed by the composition (Mühle and Williams) and also the size of a nu-Tamari lattice (Bergeron, Ceballos and Pilaud); its code counts these Dyck paths.
Called as CombinatorialStat(x, "DyckPathsAboveBouncePathCount"). The head's page has its examples.
Live
Distribution
Over IntegerCompositions at each size, tallied here in your browser; sizes past 6 are not offered.
FindStat St001312
Number of parabolic noncrossing partitions indexed by the composition.
| Object | Value |
|---|---|
[1] | 1 |
[2] | 1 |
[3] | 1 |
[4] | 1 |
[5] | 1 |
[6] | 1 |
[7] | 1 |
[8] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001312 has the rest.