Symmetries of power-free integers in number fields and their shift spaces

preprint Symmetries of power-free integers in number fields and their shift spaces Fabian Gundlach author 100450 Jürgen Klüners author 21202 We describe the group of $\mathbb Z$-linear automorphisms of the ring of integers of a number field $K$ that preserve the set $V_{K,k}$ of $k$th power-free integers: every such map is the composition of a field automorphism and the multiplication by a unit. We show that those maps together with translations generate the extended symmetry group of the shift space $\mathbb D_{K,k}$ associated to $V_{K,k}$. Moreover, we show that no two such dynamical systems $\mathbb D_{K,k}$ and $\mathbb D_{L,l}$ are topologically conjugate and no one is a factor system of another. We generalize the concept of $k$th power-free integers to sieves and study the resulting admissible shift spaces. 2024 eng arXiv:2407.08438 2407.08438 Gundlach F, Klüners J. Symmetries of power-free integers in number fields and their shift spaces. arXiv:240708438. Published online 2024. F. Gundlach and J. Klüners, “Symmetries of power-free integers in number fields and their shift spaces,” arXiv:2407.08438. 2024. Gundlach, Fabian, and Jürgen Klüners. “Symmetries of Power-Free Integers in Number Fields and Their Shift Spaces.” ArXiv:2407.08438, 2024. Gundlach, F., & Klüners, J. (2024). Symmetries of power-free integers in number fields and their shift spaces. In arXiv:2407.08438. Gundlach, Fabian, and Jürgen Klüners. “Symmetries of Power-Free Integers in Number Fields and Their Shift Spaces.” ArXiv:2407.08438, 2024. @article{Gundlach_Klüners_2024, title={Symmetries of power-free integers in number fields and their shift spaces}, journal={arXiv:2407.08438}, author={Gundlach, Fabian and Klüners, Jürgen}, year={2024} } F. Gundlach, J. Klüners, ArXiv:2407.08438 (2024). 551922024-07-12T08:16:37Z2024-07-12T08:19:11Z