DinvDeficit on DyckPath
The binomial(n, 2) less the area and the dinv: the boxes of the partition traced out by the path where leg minus arm is not 0 or 1.
Called as CombinatorialStat(x, "DinvDeficit"). 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 St000369
The dinv deficit of a Dyck path.
| Object | Value |
|---|---|
[1,0,1,0] | 0 |
[1,1,0,0] | 0 |
[1,0,1,0,1,0] | 0 |
[1,0,1,1,0,0] | 1 |
[1,1,0,0,1,0] | 0 |
[1,1,0,1,0,0] | 0 |
[1,1,1,0,0,0] | 0 |
[1,0,1,0,1,0,1,0] | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000369 has the rest.