\begin{definition}[Definition:Parity of Permutation]
Let $n \in \N$ be a natural number.
Let $S_n$ denote the symmetric group on $n$ letters.
Let $\rho \in S_n$, that is, let $\rho$ be a permutation of $S_n$.
The '''parity''' of $\rho$ is defined as follows:
\end{definition}