PeakRectangleAreaSum on DyckPath
The sum, over consecutive peaks, of the area of the rectangle they span with the valley between them.
Positions are counted from 1; only differences enter.
Called as CombinatorialStat(x, "PeakRectangleAreaSum"). The head's page has its examples.
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FindStat St000645
The sum of the areas of the rectangles formed by two consecutive peaks and the valley in between.
| Object | Value |
|---|---|
[] | 0 |
[1,0] | 0 |
[1,0,1,0] | 1 |
[1,1,0,0] | 0 |
[1,0,1,0,1,0] | 2 |
[1,0,1,1,0,0] | 2 |
[1,1,0,0,1,0] | 2 |
[1,1,0,1,0,0] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000645 has the rest.