CenteredTunnels on DyckPath
Tunnels (an up step with its matching down step) centered on the middle of the path: positions summing to the length plus one.
Called as CombinatorialStat(x, "CenteredTunnels"). The head's page has its examples.
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Distribution
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FindStat St000117
The number of centered tunnels of a Dyck path.
| Object | Value |
|---|---|
[1,0] | 1 |
[1,0,1,0] | 0 |
[1,1,0,0] | 2 |
[1,0,1,0,1,0] | 1 |
[1,0,1,1,0,0] | 0 |
[1,1,0,0,1,0] | 0 |
[1,1,0,1,0,0] | 1 |
[1,1,1,0,0,0] | 3 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000117 has the rest.