# Definition:Even 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 $S_n$.

Then $\rho$ is an even permutation if and only if:

$\map \sgn \rho = 1$

where $\sgn$ denotes the sign function.