4

GroupOrbits[CyclicGroup[5], {{1, 1, 2, 3, 3}}, Permute] {{{1, 1, 2, 3, 3}, {1, 2, 3, 3, 1}, {2, 3, 3, 1, 1}, {3, 1, 1, 2, 3}, {3, 3, 1, 1, 2}}}


1

After some clarification I think an orbit in the sense explained above can be found by repeating a right or left rotation n-1 times where n is the length of the list. This may produce identical lists (e.g. {1,2,1,2} shifted twice), therefore, we must weed out the duplicates, what can be done by DeleteDuplicates: n = 5; DeleteDuplicates[NestList[RotateRight, {...


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