\section{Definition and Notation}

\begin{definition}[Permutation of $\mathbf{A}$, Permutation Group of $\mathbf{A}$]
	A \textit{permutation} of a set $A$ is a function from $A$ to $A$ that is both one-to-one and onto. A \textit{permutation group} of a set $A$ is a set of permutations of $A$ that forms a group under function composition.
\end{definition}