UpStepsAtEvenPositions on DyckPath
Up steps at an even position, counting from 1.
Called as CombinatorialStat(x, "UpStepsAtEvenPositions"). The head's page has its examples.
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Distribution
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FindStat St000329
The number of evenly positioned ascents of the Dyck path, with the initial position equal to 1.
| Object | Value |
|---|---|
[1,0] | 0 |
[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] | 2 |
[1,1,1,0,0,0] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000329 has the rest.