DoubleDeficiencies on Permutation

Positions with i > p(i) > p(p(i)).

On Permutation

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

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Distribution

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FindStat St000732

The number of double deficiencies of a permutation.

The number of double deficiencies of a permutation. A double deficiency is an index $\sigma(i)$ such that $i > \sigma(i) > \sigma(\sigma(i))$.

Object	Value
[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]	1
[3,2,1]	0

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000732 has the rest.