Fixed points of powers of permutations

Let $\sigma$ be a permutation of a finite or countably infinite set $X$ and let $FP(\sigma)$ be the number of fixed points of $\sigma$. This talk describes how the sequence $\left(FP\left( \sigma^k\right) \right)_{k=1}^{\infty}$ determines the permutation $\sigma$ and how it interacts with certain arithmetic functions..

Mel Nathanson