# Definition:Rotation (Permutation Theory)

Let $\tuple {a_1, \ldots, a_n}$ be a string over an alphabet $A$.
A rotation is a mapping $r: A^n \to A^n$ given by:
$\tuple {a_1, \ldots, a_n} \mapsto \tuple {a_{\map \phi 1}, \cdots, a_{\map \phi n} }$
where $\phi$ is a permutation on n letters.