CylindricalTableauOverlap on StandardTableau
The number of rows, from the top, as long as the first row and starting, from the bottom, above the last entry of the first row.
The overlap of the cylindrical tableau built from two copies (FindStat's St001803). The empty tableau gives 0.
Called as CombinatorialStat(x, "CylindricalTableauOverlap"). 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 St001803
The maximal overlap of the cylindrical tableau associated with a tableau.
| Object | Value |
|---|---|
[[1]] | 0 |
[[1,2]] | 0 |
[[1,2,3]] | 0 |
[[1],[2]] | 1 |
[[1,2,3,4]] | 0 |
[[1,2],[3]] | 1 |
[[1,3],[2]] | 0 |
[[1,2,3,4,5]] | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001803 has the rest.