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OddInversions on Permutation ​

Inversions i < j with j - i odd.

On Permutation

Called as CombinatorialStat(x, "OddInversions"). The head's page has its examples.

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Distribution

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FindStat St000539

The number of odd inversions of a permutation.

ObjectValue
[1,2]0
[2,1]1
[1,2,3]0
[1,3,2]1
[2,1,3]1
[2,3,1]1
[3,1,2]1
[3,2,1]2

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000539 has the rest.