Definition:Odd Permutation
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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 $S_n$.
Definition 1
$\rho$ is an odd permutation if and only if $\rho$ is equivalent to an odd number of transpositions.
Definition 2
$\rho$ is an odd permutation if and only if:
- $\map \sgn \rho = -1$
where $\sgn$ denotes the sign function.
Also see
- Results about odd permutations can be found here.