English

On arithmetic progressions in model sets

Dynamical Systems 2021-01-27 v1 Mathematical Physics math.MP

Abstract

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

Keywords

Cite

@article{arxiv.2003.13860,
  title  = {On arithmetic progressions in model sets},
  author = {Anna Klick and Nicolae Strungaru and Adi Tcaciuc},
  journal= {arXiv preprint arXiv:2003.13860},
  year   = {2021}
}

Comments

17 pages, 2 figures