PyramidWeight on DyckPath

Over each peak, the shorter of the up run before it and the down run after it, summed: the sizes of the maximal pyramids.

On DyckPath

Called as CombinatorialStat(x, "PyramidWeight"). 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.

Sizes 1 to

FindStat St000144

The pyramid weight of the Dyck path.

Object	Value
[1,0]	1
[1,0,1,0]	2
[1,1,0,0]	2
[1,0,1,0,1,0]	3
[1,0,1,1,0,0]	3
[1,1,0,0,1,0]	3
[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/St000144 has the rest.