LatticePathsAboveWordCount on BinaryWord
The paths of the word's length, ending anywhere, that stay weakly above the path the word gives.
FindStat's St001365. A 1 is a step up and a 0 a step across; a path is above when it has made at least as many steps up after every step. The fold counts the paths by how many steps up they are ahead.
Called as CombinatorialStat(x, "LatticePathsAboveWordCount"). The head's page has its examples.
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Distribution
Over BinaryWords at each size, tallied here in your browser; sizes past 6 are not offered.
FindStat St001365
The number of lattice paths of the same length weakly above the path given by a binary word.
| Object | Value |
|---|---|
0 | 2 |
1 | 1 |
00 | 4 |
01 | 3 |
10 | 2 |
11 | 1 |
000 | 8 |
001 | 7 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001365 has the rest.