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| Main Author: | |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2206.04021 |
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Table of Contents:
- 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.