InverseDescentParkingFunctionCount on IntegerComposition
Parking functions of size n whose diagonal reading word has the inverse descent composition c.
FindStat's St000285 is the size of that preimage; the count here is the equivalent word count, 1/(n+1) of the words on 1 .. n+1 that fall within each block and rise between blocks.
Called as CombinatorialStat(x, "InverseDescentParkingFunctionCount"). 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 St000285
The size of the preimage of the map 'to inverse des composition' from Parking functions to Integer compositions.
| Object | Value |
|---|---|
[2] | 1 |
[3] | 1 |
[4] | 1 |
[5] | 1 |
[6] | 1 |
[7] | 1 |
[8] | 1 |
[9] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000285 has the rest.