Cocharge on StandardTableau
The cocharge of the reading word: the sum of n - e over the entries e whose successor is in a lower row.
The charge and the cocharge add to n(n - 1) / 2.
Called as CombinatorialStat(x, "Cocharge"). 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 St000169
The cocharge 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]] | 2 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000169 has the rest.