Inversions on Permutation
Pairs i < j with p(i) > p(j).
Called as CombinatorialStat(x, "Inversions"). The head's page has its examples.
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The same name on other carriers, each its own implementation: IntegerComposition, BinaryWord.
FindStat St000018
The number of inversions of a permutation.
| Object | Value |
|---|---|
[] | 0 |
[1] | 0 |
[1,2] | 0 |
[2,1] | 1 |
[1,2,3] | 0 |
[1,3,2] | 1 |
[2,1,3] | 1 |
[2,3,1] | 2 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000018 has the rest.