AdjacentSuccessorCount on StandardTableau
Entries whose successor is the neighbor to their right or directly below them.
Consecutive entries of a row or a column are always neighbors, so this counts the entries e with e + 1 in the same row or the same column.
Called as CombinatorialStat(x, "AdjacentSuccessorCount"). The head's page has its examples.
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Distribution
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FindStat St000743
The number of entries in a standard Young tableau such that the next integer is a neighbour.
| Object | Value |
|---|---|
[] | 0 |
[[1]] | 0 |
[[1,2]] | 1 |
[[1,2,3]] | 2 |
[[1],[2]] | 1 |
[[1,2,3,4]] | 3 |
[[1,2],[3]] | 1 |
[[1,3],[2]] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000743 has the rest.