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\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}