AttackingPairCount on StandardTableau
Pairs of cells of the shape with one strictly west of the other in a row, or the first in the row below and strictly east of the second.
A cell with k cells west of it in its row makes k pairs there and k more with the row above, if it has a row above. It depends on the shape alone (FindStat's St000016). The empty tableau gives 0.
Called as CombinatorialStat(x, "AttackingPairCount"). 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 St000016
The number of attacking pairs of a standard tableau.
| Object | Value |
|---|---|
[[1]] | 0 |
[[1,2]] | 1 |
[[1,2,3]] | 3 |
[[1],[2]] | 0 |
[[1,2,3,4]] | 6 |
[[1,2],[3]] | 1 |
[[1,3],[2]] | 1 |
[[1,2,3,4,5]] | 10 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000016 has the rest.