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LargestAreaSequenceEntry on DyckPath ​

The largest entry of the area sequence: the greatest area to the right of an up step.

On DyckPath

Called as CombinatorialStat(x, "LargestAreaSequenceEntry"). 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 St000442

The maximal area to the right of an up step of a Dyck path.

ObjectValue
[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]1
[1,1,1,0,0,0]2
[1,0,1,0,1,0,1,0]0

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000442 has the rest.