ValleysAboveAxis on DyckPath
Valleys not on the axis: a down step followed by an up step, at height above 0.
Called as CombinatorialStat(x, "ValleysAboveAxis"). 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 St000052
The number of valleys of a Dyck path not on the x-axis.
| Object | Value |
|---|---|
[] | 0 |
[1,0] | 0 |
[1,0,1,0] | 0 |
[1,1,0,0] | 0 |
[1,0,1,0,1,0] | 0 |
[1,0,1,1,0,0] | 0 |
[1,1,0,0,1,0] | 0 |
[1,1,0,1,0,0] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000052 has the rest.