MajorIndexMinusWeightedSize on StandardTableau
The major index of the tableau less the weighted size of its shape.
FindStat's St001699. The major index is the sum of the descents, the entries whose successor is in a strictly lower row; the weighted size is the sum over the rows of the row's number counted from 0 times its length. A tableau of fewer than two entries has neither.
Called as CombinatorialStat(x, "MajorIndexMinusWeightedSize"). The head's page has its examples.
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Distribution
Over StandardTableaux at each size, tallied here in your browser; sizes past 6 are not offered.
FindStat St001699
The major 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]] | 1 |
[[1,3],[2]] | 0 |
[[1,2,3,4,5]] | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001699 has the rest.