Definition:Parity of Permutation

Definition
Let $n \in \N$ be a natural number.

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

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

The parity of $\rho$ is defined as follows:

Odd Permutation
where $\map \sgn \rho$ denotes the sign of $\rho$.

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