GlobalMaxima on DyckPath
The number of points of the path at the greatest height it reaches.
The origin counts as a point, so the empty path has one; otherwise these are its highest peaks.
Called as CombinatorialStat(x, "GlobalMaxima"). 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 St000617
The number of global maxima of a Dyck path.
| Object | Value |
|---|---|
[] | 1 |
[1,0] | 1 |
[1,0,1,0] | 2 |
[1,1,0,0] | 1 |
[1,0,1,0,1,0] | 3 |
[1,0,1,1,0,0] | 1 |
[1,1,0,0,1,0] | 1 |
[1,1,0,1,0,0] | 2 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000617 has the rest.