MajorIndex on Permutation
The SUM of the descent positions — not their count.
The distinction from Descents is the entire content of the statistic.
Called as CombinatorialStat(x, "MajorIndex"). The head's page has its examples.
Live
Also on
The same name on other carriers, each its own implementation: DyckPath.
FindStat St000004
The major index of a permutation.
| Object | Value |
|---|---|
[] | 0 |
[1] | 0 |
[1,2] | 0 |
[2,1] | 1 |
[1,2,3] | 0 |
[1,3,2] | 2 |
[2,1,3] | 1 |
[2,3,1] | 2 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000004 has the rest.