On higher dimensional arithmetic progressions in Meyer sets
| dc.contributor.author | Klick, Anna | |
| dc.contributor.author | Strungaru, Nicolae | |
| dc.date.accessioned | 2024-01-23T18:06:34Z | |
| dc.date.available | 2024-01-23T18:06:34Z | |
| dc.date.issued | 2023 | |
| dc.description.abstract | In 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. | |
| dc.identifier.citation | Klick, A., & Strungaru, N. (2023). On higher dimensional arithmetic progressions in Meyer sets. arXiv:2103.05049 [math.NT]. https://arxiv.org/abs/2103.05049 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14078/3385 | |
| dc.language.iso | en | |
| dc.rights | All Rights Reserved | |
| dc.subject | Meyer sets | |
| dc.subject | arithmetic progressions | |
| dc.title | On higher dimensional arithmetic progressions in Meyer sets | en |
| dc.type | Article Post-Print |
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