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 $S_n$.

Then $\rho$ is an odd permutation :
 * $\operatorname{sgn} \left({\rho}\right) = -1$

where $\operatorname{sgn}$ denotes the sign function.

Also see

 * Definition:Even Permutation