Definition:Rotation (Permutation Theory)

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Definition

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.