NonInversionSum on Permutation
The sum of j - i over the non-inversions i < j.
Called as CombinatorialStat(x, "NonInversionSum"). The head's page has its examples.
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The same name on other carriers, each its own implementation: BinaryWord.
FindStat St000341
The non-inversion sum of a permutation.
| Object | Value |
|---|---|
[1] | 0 |
[1,2] | 1 |
[2,1] | 0 |
[1,2,3] | 4 |
[1,3,2] | 3 |
[2,1,3] | 3 |
[2,3,1] | 1 |
[3,1,2] | 1 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000341 has the rest.