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

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

Also see

 * Parity Group.