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:
$\rho$ is an even permutation if and only if:
- $\map \sgn \rho = 1$
$\rho$ is an odd permutation if and only if:
- $\map \sgn \rho = -1$
where $\map \sgn \rho$ denotes the sign of $\rho$.
Also defined as