# Definition:Odd Permutation

## Definition

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 odd permutation if and only if:

$\map \sgn \rho = -1$

where $\sgn$ denotes the sign function.