MajorIndex on IntegerComposition
The sum of the positions i with c(i) > c(i+1).
MacMahon's major index of the composition regarded as a word.
Called as CombinatorialStat(x, "MajorIndex"). The head's page has its examples.
Live
Distribution
Over IntegerCompositions at each size, tallied here in your browser; sizes past 6 are not offered.
Also on
The same name on other carriers, each its own implementation: Permutation, DyckPath, BinaryWord.
FindStat St000769
The major index of a composition regarded as a word.
| Object | Value |
|---|---|
[] | 0 |
[1] | 0 |
[2] | 0 |
[3] | 0 |
[4] | 0 |
[5] | 0 |
[6] | 0 |
[7] | 0 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000769 has the rest.