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ThreeShiftedMajorIndex on Permutation ​

The sum of the positions i with p(i) - p(i+1) > 3.

On Permutation

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

Live

Distribution

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FindStat St000962

The 3-shifted major index of a permutation.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000962 has the rest.