LeftTunnels on DyckPath
Tunnels (an up step with its matching down step) left of the middle: positions summing to less than the length plus one.
Called as CombinatorialStat(x, "LeftTunnels"). 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 St000120
The number of left tunnels of a Dyck path.
| Object | Value |
|---|---|
[1,0] | 0 |
[1,0,1,0] | 1 |
[1,1,0,0] | 0 |
[1,0,1,0,1,0] | 1 |
[1,0,1,1,0,0] | 1 |
[1,1,0,0,1,0] | 2 |
[1,1,0,1,0,0] | 1 |
[1,1,1,0,0,0] | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000120 has the rest.