If one is given the length of a permutation and the number of cycles, is it possible to determine the parity of the permutation?
Oddly enough, there's no definition in the text I'm reading for cycle decomposition. I'm assuming it means the permutation $\sigma$ written as a product of disjoint cycles.
I also know a permutation is odd if and only if there are an odd number of even length cycles. (But I know this because of Wikipedia.)
So how does one determine the parity of a permutation?