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MinimalCycleDifference on Permutation ​

The smallest, over the cycles, of the largest difference between two elements of a cycle.

On Permutation

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

Live

Distribution

Over SymmetricGroup at each size, tallied here in your browser; sizes past 8 are not offered.

FindStat St000210

Minimum over maximum difference of elements in cycles.

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

Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000210 has the rest.