CornerMajorIndex on IntegerPartition
The sum, over the corners, of the step number along the boundary path from the bottom left: (number of parts - i) + the i-th part.
For (8, 6, 6, 4, 3, 3) the corners are at steps 3, 6, 9 and 13, so the value is 31 (FindStat's St000770 example).
Called as CombinatorialStat(x, "CornerMajorIndex"). 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 St000770
The major index of an integer partition when read from bottom to top.
| Object | Value |
|---|---|
[2] | 2 |
[3] | 3 |
[4] | 4 |
[5] | 5 |
[6] | 6 |
[7] | 7 |
[8] | 8 |
[9] | 9 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000770 has the rest.