Fixed points of powers of permutations

Melvyn B. Nathanson

Published 2022-06-08Version 1

Let $\sigma$ be a permutation of a finite or infinite set $X$, and let $F_X\left( \sigma^k\right)$ be the number of fixed points of the $k$th power of $\sigma$. This paper describes how the sequence $\left(F_X\left( \sigma^k\right) \right)_{k=1}^{\infty}$ determines the permutation $\sigma$.