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arXiv · 2003.13860

On arithmetic progressions in model sets

Anna Klick·Nicolae Strungaru·Adi Tcaciuc
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Abstract

In this project we show the existence of arbitrary length arithmetic progressions in model sets and Meyer sets in the Euclidean $d$-space. We prove a van der Waerden type theorem for Meyer sets. We show that pure point subsets of Meyer sets with positive density and pure point diffraction contain arithmetic progressions of arbitrary length.

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Anna Klick, Nicolae Strungaru, Adi Tcaciuc. 2020-03-30. On arithmetic progressions in model sets. https://doi.org/10.1007/s00454-020-00252-6

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