Charge on StandardTableau
The charge of the reading word: the sum of n - e over the entries e whose successor is not in a lower row.
The reading word lists the rows from the bottom up, so e + 1 is to the right of e exactly when its row is not lower. The charge of a standard word adds, for each e with e + 1 to its right, the n - e entries from e + 1 on.
Called as CombinatorialStat(x, "Charge"). 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 St000009
The charge of a standard tableau.
| Object | Value |
|---|---|
[] | 0 |
[[1]] | 0 |
[[1,2]] | 1 |
[[1,2,3]] | 3 |
[[1],[2]] | 0 |
[[1,2,3,4]] | 6 |
[[1,2],[3]] | 2 |
[[1,3],[2]] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000009 has the rest.