TwiceMeanMajorIndexOfStandardTableaux on IntegerPartition
Twice the mean major index over the standard tableaux: n choose 2, less the sum of the row lengths choose 2, plus the sum of the column lengths choose 2.
Called as CombinatorialStat(x, "TwiceMeanMajorIndexOfStandardTableaux"). The head's page has its examples.
Live
Distribution
Over IntegerPartitions at each size, tallied here in your browser; sizes past 30 are not offered.
FindStat St001177
Twice the mean value of the major index among all standard Young tableaux of a partition.
| Object | Value |
|---|---|
[1] | 0 |
[2] | 0 |
[3] | 0 |
[4] | 0 |
[5] | 0 |
[6] | 0 |
[7] | 0 |
[8] | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001177 has the rest.