Definition:Parity of Permutation

Definition
Let $S_n$ denote the symmetric group on $n$ letters.

Let $\pi \in S_n$, that is, let $\pi$ be a permutation of $S_n$.

The parity of $\pi$ is defined as:


 * Parity of $\pi = \begin{cases}

\operatorname {Even} & : \operatorname{sgn} \left({\pi}\right) = 1 \\ \operatorname {Odd} & : \operatorname{sgn} \left({\pi}\right) = -1 \end{cases}$

where $\operatorname{sgn} \left({\pi}\right)$ is the sign of $\pi$.

Also defined as
Some sources define the parity of a permutation as defines its sign: that is, as $1$ and $-1$.

Also see

 * Definition:Parity Group


 * Parity Group is Group
 * Parity Function is Homomorphism