On arithmetic progressions in model sets

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.

arXiv comment17 pages, 2 figures

References in corpus (13)

• Dynamical systems on translation bounded measures: Pure point dynamical and diffraction spectra
• Characterizations of model sets by dynamical systems
• Dynamics on the graph of the torus parametrisation
• Pure point diffraction and cut and project schemes for measures: The smooth case
• Dense Dirac combs in Euclidean space with pure point diffraction
• Pure point diffraction and Poisson summation
• On the Fourier Analysis of Measures with Meyer Set Support
• Pure Point Diffraction and Mean, Besicovitch and Weyl Almost Periodicity
• Almost Periodic Measures and Meyer Sets
• On Weakly Almost Periodic Measures
• On Weighted Dirac Combs Supported Inside Model Sets
• On the Bragg Diffraction Spectra of a Meyer Set
• A note on measures vanishing at infinity

Cited by in corpus (3)

• On arithmetic progressions in non-periodic self-affine tilings
• Why do Meyer sets diffract?
• A Szemerédi type theorem for sets of positive density in approximate lattices