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MaximalCycleDifference on Permutation ​

The largest difference between two elements of one cycle.

On Permutation

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

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Distribution

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FindStat St000209

Maximum difference of elements in cycles.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000209 has the rest.