SameEndpointPathsAboveWordCount on BinaryWord
The paths with the word's number of ones and zeros that stay weakly above the path the word gives.
FindStat's St001313, the count of St001365 that end where the word does: ahead by 0 steps up.
Called as CombinatorialStat(x, "SameEndpointPathsAboveWordCount"). The head's page has its examples.
Live
Distribution
Over BinaryWords at each size, tallied here in your browser; sizes past 6 are not offered.
FindStat St001313
The number of Dyck paths above the lattice path given by a binary word.
| Object | Value |
|---|---|
0 | 1 |
1 | 1 |
00 | 1 |
01 | 2 |
10 | 1 |
11 | 1 |
000 | 1 |
001 | 3 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001313 has the rest.