\begin{definition}[Definition:Even Permutation]
Let $n \in \N$ be a natural number.
Let $S_n$ denote the symmetric group on $n$ letters.
Let $\rho \in S_n$ be a permutation in $S_n$.
$\rho$ is an '''even permutation''' {{iff}}:
:$\map \sgn \rho = 1$
where $\sgn$ denotes the sign function.
\end{definition}