Gespeichert in:
Bibliographische Detailangaben
1. Verfasser: Nathanson, Melvyn B.
Format: Preprint
Veröffentlicht: 2022
Schlagworte:
Online-Zugang:https://arxiv.org/abs/2206.04021
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Inhaltsangabe:
  • Let $σ$ be a permutation of a nonempty finite or countably infinite set $X$ and let $F_X\left( σ^k\right)$ count the number of fixed points of the $k$th power of $σ$. This paper explains how the arithmetic function $k \mapsto \left(F_X\left( σ^k\right) \right)_{k=1}^{\infty}$ determines the conjugacy class of the permutation $σ$, constructs an algorithm to compute the conjugacy class from the fixed point counting function $F_X\left( σ^k\right)$, and describes the arithmetic functions that are fixed point counting functions of permutations.