FirstColumnInitialSequenceLength on StandardTableau
The largest k such that the first column starts 1, 2, ..., k.
FindStat's title is the index of the last row whose first entry is the row number (St000745).
Called as CombinatorialStat(x, "FirstColumnInitialSequenceLength"). The head's page has its examples.
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FindStat St000745
The index of the last row whose first entry is the row number in a standard Young tableau.
| Object | Value |
|---|---|
[] | 0 |
[[1]] | 1 |
[[1,2]] | 1 |
[[1,2,3]] | 1 |
[[1],[2]] | 2 |
[[1,2,3,4]] | 1 |
[[1,2],[3]] | 1 |
[[1,3],[2]] | 2 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000745 has the rest.