Klick, AnnaStrungaru, Nicolae2024-01-232024-01-232023Klick, A., & Strungaru, N. (2023). On higher dimensional arithmetic progressions in Meyer sets. arXiv:2103.05049 [math.NT]. https://arxiv.org/abs/2103.05049https://hdl.handle.net/20.500.14078/3385In this paper we study the existence of higher dimensional arithmetic progression in Meyer sets. We show that the case when the ratios are linearly dependent over $\ZZ$ is trivial, and focus on arithmetic progressions for which the ratios are linearly independent. Given a Meyer set Λ and a fully Euclidean model set $\oplam(W)$ with the property that finitely many translates of $\oplam(W)$ cover Λ, we prove that we can find higher dimensional arithmetic progressions of arbitrary length with k linearly independent ratios in Λ if and only if k is at most the rank of the $\ZZ$-module generated by $\oplam(W)$. We use this result to characterize the Meyer sets which are subsets of fully Euclidean model sets.enAll Rights ReservedMeyer setsarithmetic progressionsArticle Post-Print