Parity of a Permutation
A permutation is even when and odd when .
Definition 8.16 (Parity of a Permutation)
If , then is called an even permutation. Otherwise, it is called an odd permutation.
Examples
A -cycle is even if and only if is odd. More generally, a permutation of cycle type is even if and only if an even number of the are even. For example, is even, while is odd.
Related
Stated in
- Definition 8.16 (Parity of a Permutation)§8.2 Transpositions and the Sign Homomorphism