ParkingFunctionCount on DyckPath
The parking functions supported by the path: semilength factorial over the product of the factorials of the rise lengths.
A parking function is a path with the cars of each column labeled; the labels must increase up each rise, which leaves n!/(r_1! r_2! ...) of them.
Called as CombinatorialStat(x, "ParkingFunctionCount"). 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 St000014
The number of parking functions supported by a Dyck path.
| Object | Value |
|---|---|
[1,0] | 1 |
[1,0,1,0] | 2 |
[1,1,0,0] | 1 |
[1,0,1,0,1,0] | 6 |
[1,0,1,1,0,0] | 3 |
[1,1,0,0,1,0] | 3 |
[1,1,0,1,0,0] | 3 |
[1,1,1,0,0,0] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000014 has the rest.