SetValuedTableauNaturalDescents on DyckPath
The natural descents of the set-valued two-row tableau the path corresponds to, read off the step pairs by FindStat's rules.
FindStat's St001955. The rules go through bicolored Motzkin paths; they are stated on the path itself and implemented as given.
Called as CombinatorialStat(x, "SetValuedTableauNaturalDescents"). The head's page has its examples.
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FindStat St001955
The number of natural descents for set-valued two row standard Young tableaux.
| Object | Value |
|---|---|
[1,0] | 0 |
[1,0,1,0] | 1 |
[1,1,0,0] | 1 |
[1,0,1,0,1,0] | 2 |
[1,0,1,1,0,0] | 1 |
[1,1,0,0,1,0] | 2 |
[1,1,0,1,0,0] | 2 |
[1,1,1,0,0,0] | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001955 has the rest.