WeightedSize on StandardTableau
The sum of the leg lengths of the cells, the sum over the cells of their row counted from 0.
FindStat's leg major index (St000336), a statistic of the shape; on a partition it is the same head. The empty tableau gives 0.
Called as CombinatorialStat(x, "WeightedSize"). 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.
Also on
The same name on other carriers, each its own implementation: IntegerPartition.
FindStat St000336
The leg major index of a standard tableau.
| Object | Value |
|---|---|
[] | 0 |
[[1]] | 0 |
[[1,2]] | 0 |
[[1,2,3]] | 0 |
[[1],[2]] | 1 |
[[1,2,3,4]] | 0 |
[[1,2],[3]] | 1 |
[[1,3],[2]] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000336 has the rest.