BicoloredMotzkinHeight on DyckPath
The height of the bicolored Motzkin path made by reading the steps in pairs: two up steps rise, two down steps fall.
Called as CombinatorialStat(x, "BicoloredMotzkinHeight"). 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 St001031
The height of the bicoloured Motzkin path associated with the Dyck path.
| Object | Value |
|---|---|
[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] | 1 |
[1,0,1,0,1,0,1,0] | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001031 has the rest.