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BigDeficiencies on Permutation ​

Positions with i - p(i) > 1.

On Permutation

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

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Distribution

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FindStat St000710

The number of big deficiencies 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]1
[3,1,2]0
[3,2,1]1

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000710 has the rest.