{"external_id":{"arxiv":["2407.08438"]},"type":"preprint","publication":"arXiv:2407.08438","date_created":"2024-07-12T08:16:37Z","user_id":"82981","status":"public","abstract":[{"lang":"eng","text":"We describe the group of $\\mathbb Z$-linear automorphisms of the ring of\r\nintegers of a number field $K$ that preserve the set $V_{K,k}$ of $k$th\r\npower-free integers: every such map is the composition of a field automorphism\r\nand the multiplication by a unit.\r\n  We show that those maps together with translations generate the extended\r\nsymmetry group of the shift space $\\mathbb D_{K,k}$ associated to $V_{K,k}$.\r\nMoreover, we show that no two such dynamical systems $\\mathbb D_{K,k}$ and\r\n$\\mathbb D_{L,l}$ are topologically conjugate and no one is a factor system of\r\nanother.\r\n  We generalize the concept of $k$th power-free integers to sieves and study\r\nthe resulting admissible shift spaces."}],"author":[{"full_name":"Gundlach, Fabian","id":"100450","last_name":"Gundlach","first_name":"Fabian"},{"full_name":"Klüners, Jürgen","id":"21202","first_name":"Jürgen","last_name":"Klüners"}],"citation":{"chicago":"Gundlach, Fabian, and Jürgen Klüners. “Symmetries of Power-Free Integers in Number Fields and Their Shift  Spaces.” <i>ArXiv:2407.08438</i>, 2024.","bibtex":"@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} }","mla":"Gundlach, Fabian, and Jürgen Klüners. “Symmetries of Power-Free Integers in Number Fields and Their Shift  Spaces.” <i>ArXiv:2407.08438</i>, 2024.","ieee":"F. Gundlach and J. Klüners, “Symmetries of power-free integers in number fields and their shift  spaces,” <i>arXiv:2407.08438</i>. 2024.","ama":"Gundlach F, Klüners J. Symmetries of power-free integers in number fields and their shift  spaces. <i>arXiv:240708438</i>. Published online 2024.","short":"F. Gundlach, J. Klüners, ArXiv:2407.08438 (2024).","apa":"Gundlach, F., &#38; Klüners, J. (2024). Symmetries of power-free integers in number fields and their shift  spaces. In <i>arXiv:2407.08438</i>."},"_id":"55192","title":"Symmetries of power-free integers in number fields and their shift  spaces","language":[{"iso":"eng"}],"year":"2024","date_updated":"2024-07-12T08:19:11Z"}