CenteredMultitunnels on DyckPath

Factorizations of the path into three parts, the middle one a Dyck path and the outer two of equal length.

On DyckPath

Called as CombinatorialStat(x, "CenteredMultitunnels"). 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 St000675

The number of centered multitunnels of a Dyck path.

Object	Value
[1,0,1,0]	1
[1,1,0,0]	2
[1,0,1,0,1,0]	2
[1,0,1,1,0,0]	1
[1,1,0,0,1,0]	1
[1,1,0,1,0,0]	2
[1,1,1,0,0,0]	3
[1,0,1,0,1,0,1,0]	2

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000675 has the rest.