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MaximalModularDisplacement on Permutation ​

The largest cyclic distance between p(i) and i, taken mod n.

On Permutation

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

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Distribution

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FindStat St001569

The maximal modular displacement 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]1

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St001569 has the rest.