Definition:Composite Defined by Permutation

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

Let $\left\langle{a_k}\right\rangle_{k \mathop \in A}$ 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 $\left\langle{a_{\sigma \left({k}\right)}}\right\rangle_{k \mathop \in A}$ is defined as: