Definition:Composite Defined by Permutation

Definition
Let $\oplus$ be an $n$-ary operation on a set $S$.

Let $\sequence {a_k}_{k \mathop \in A}$ be a sequence of $n$ terms of $S$.

Let $\sigma: A \to A$ be a permutation of $A$.

Then the composite of the ordered $n$-tuple defined by the sequence $\sequence {a_{\map \sigma k} }_{k \mathop \in A}$ is defined as: