HaglundStevensInversionCount on StandardTableau
The pairs of a cell's entry and a smaller entry lying below the cell's inversion path, over all cells.
FindStat's St000059, Haglund and Stevens's inversion number. The inversion path of a cell leaves it up when the entry above is larger than the entry to the left, else left, until it reaches the first column (and then runs straight up) or the first row; the cells below the path in a row are those from the path's column on. A path has fewer than n steps and stays put once it ends.
Called as CombinatorialStat(x, "HaglundStevensInversionCount"). 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 St000059
The inversion number of a standard tableau as defined by Haglund and Stevens.
| Object | Value |
|---|---|
[] | 0 |
[[1]] | 0 |
[[1,2]] | 0 |
[[1,2,3]] | 0 |
[[1],[2]] | 1 |
[[1,2,3,4]] | 0 |
[[1,2],[3]] | 2 |
[[1,3],[2]] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000059 has the rest.