SetValuedTableauComajorIndex on DyckPath
The comajor index of the set-valued two-row tableau the path corresponds to: the sum, over its natural descents k, of the semilength plus one less k.
FindStat's St001956; the natural descents are those of SetValuedTableauNaturalDescents.
Called as CombinatorialStat(x, "SetValuedTableauComajorIndex"). The head's page has its examples.
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FindStat St001956
The comajor index for set-valued two-row standard Young tableaux.
| Object | Value |
|---|---|
[1,0] | 0 |
[1,0,1,0] | 0 |
[1,1,0,0] | 1 |
[1,0,1,0,1,0] | 1 |
[1,0,1,1,0,0] | 2 |
[1,1,0,0,1,0] | 2 |
[1,1,0,1,0,0] | 3 |
[1,1,1,0,0,0] | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001956 has the rest.