PathLengthToLargestEntry on StandardTableau
The length of the path from the top left cell to the largest entry, one step per cell down or to the right.
FindStat sums the 0-based row and column of the cell. The empty tableau, which has no such entry, gives 0.
Called as CombinatorialStat(x, "PathLengthToLargestEntry"). The head's page has its examples.
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FindStat St000744
The length of the path to the largest entry in a standard Young tableau.
| Object | Value |
|---|---|
[[1,2]] | 1 |
[[1,2,3]] | 2 |
[[1],[2]] | 1 |
[[1,2,3,4]] | 3 |
[[1,2],[3]] | 1 |
[[1,3],[2]] | 1 |
[[1,2,3,4,5]] | 4 |
[[1,2,3],[4]] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000744 has the rest.