paper

On arithmetic progressions in model sets

arXiv:2003.13860 · doi:10.1007/s00454-020-00252-6

Abstract

In this project we show the existence of arbitrary length arithmetic progressions in model sets and Meyer sets in the Euclidean -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.

17 pages, 2 figures

On arithmetic progressions in model sets · wovepaper