HillsOfSizeTwo on DyckPath
Occurrences of two up steps then two down steps, starting on the axis.
Called as CombinatorialStat(x, "HillsOfSizeTwo"). The head's page has its examples.
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Distribution
Over DyckPaths at each size, tallied here in your browser; sizes past 10 are not offered.
FindStat St001139
The number of occurrences of hills of size 2 in a Dyck path.
| Object | Value |
|---|---|
[1,0,1,0] | 0 |
[1,1,0,0] | 1 |
[1,0,1,0,1,0] | 0 |
[1,0,1,1,0,0] | 1 |
[1,1,0,0,1,0] | 1 |
[1,1,0,1,0,0] | 0 |
[1,1,1,0,0,0] | 0 |
[1,0,1,0,1,0,1,0] | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001139 has the rest.