Citation: Bartlow, T. L. "An historical note on the parity of permutations." The American Mathematical Monthly 79.7 (1972): 766-769.
Web: https://www.jstor.org/stable/2316272?seq=1
Tags: Mathematical, Expository
In this lovely little article, Bartlow gives a historical discussion surrounding the parity of permutations.
The fact that permutations have a well-defined notion of parity is a fundamental fact about permutation groups. There are many proofs of this fact. This author outlines the historical motivation for the result (namely, polynomials and the insolubility of the quintic) as well as giving a proof which is similar to the original proof of the result. The proof goes like this: every permutation can be uniquely written as a product of disjoint cycles. Adding a transposition always increases or decreases the number of cycles by 1. Thus, no permutation can be written as both an odd and even number of cycles.
This is potentially a good reference to point someone to if they are curious to learn more about the fact that permutations have parity.