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FirstMaximalPeakPosition on DyckPath ​

The position of the up step into the first peak of maximal height.

On DyckPath

Called as CombinatorialStat(x, "FirstMaximalPeakPosition"). The head's page has its examples.

Live

Distribution

Over DyckPaths at each size, tallied here in your browser; sizes past 10 are not offered.

FindStat St001809

The index of the step at the first peak of maximal height in a Dyck path.

ObjectValue
[1,0]1
[1,0,1,0]1
[1,1,0,0]2
[1,0,1,0,1,0]1
[1,0,1,1,0,0]4
[1,1,0,0,1,0]2
[1,1,0,1,0,0]2
[1,1,1,0,0,0]3

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001809 has the rest.