On arithmetic progressions in model sets

Anna Klick, Nicolae Strungaru, Adi Tcaciuc

备注：: 17 pages, 2 figures
DOI：: 10.1007/s00454-020-00252-6

英文摘要：

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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