ComajorIndexMinusWeightedSize on StandardTableau
The sum of n - e over the descents e of the tableau, less the weighted size of its shape.
FindStat's St001698. A descent is an entry whose successor is in a strictly lower row. A tableau of fewer than two entries has neither.
Called as CombinatorialStat(x, "ComajorIndexMinusWeightedSize"). The head's page has its examples.
Live
Distribution
Over StandardTableaux at each size, tallied here in your browser; sizes past 6 are not offered.
FindStat St001698
The comajor index of a standard tableau minus the weighted size of its shape.
| Object | Value |
|---|---|
[[1]] | 0 |
[[1,2]] | 0 |
[[1,2,3]] | 0 |
[[1],[2]] | 0 |
[[1,2,3,4]] | 0 |
[[1,2],[3]] | 0 |
[[1,3],[2]] | 1 |
[[1,2,3,4,5]] | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001698 has the rest.