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InversionsPlusMajorIndex on Permutation ​

The number of inversions plus the major index.

On Permutation

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

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FindStat St001379

The number of inversions plus the major index of a permutation.

ObjectValue
[1]0
[1,2]0
[2,1]2
[1,2,3]0
[1,3,2]3
[2,1,3]2
[2,3,1]4
[3,1,2]3

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001379 has the rest.