A combinatorial approach to the power of 2 in the number of involutions

Dongsu Kim, Jang Soo Kim

Published 2009-02-25, updated 2010-11-02Version 2

We provide a combinatorial approach to the largest power of $p$ in the number of permutations $\pi$ with $\pi^p=1$, for a fixed prime number $p$. With this approach, we find the largest power of $2$ in the number of involutions, in the signed sum of involutions and in the numbers of even or odd involutions.