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Cyclic Permutation


A permutation which shifts all elements of a set by a fixed offset, with the elements shifted off the end inserted back at the beginning. For a set with elements a_0, a_1, ..., a_(n-1), a cyclic permutation of one place to the left would yield a_1, ..., a_(n-1), a_0, and a cyclic permutation of one place to the right would yield a_(n-1), a_0, a_1, ....

The mapping can be written as a_i->a_(i+k (mod n)) for a shift of k places. A shift of k places to the left is implemented in the Wolfram Language as RotateLeft[list, k], while a shift of k places to the right is implemented as RotateRight[list, k].


See also

Permutation

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Cite this as:

Weisstein, Eric W. "Cyclic Permutation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CyclicPermutation.html

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