nLab
cyclic permutation

Contents

Contents

Definition

For a finite set XX, a cyclic permutation on XX is a permutation σ:XX\sigma \colon X \to X such that the induced group homomorphism Aut(X)\mathbb{Z} \to Aut(X) from the integers to the automorphism group (i.e. the symmetric group) of XX, sending nn \in \mathbb{Z} to σ n\sigma^n, defines a transitive action.

One may visualize the elements of XX as points arranged on a circle spaced equally apart, with σ(x)\sigma(x) the next-door neighbor of xx in the counterclockwise direction, hence the name.

See also rotation permutation.

Last revised on December 31, 2018 at 07:16:13. See the history of this page for a list of all contributions to it.