Klick, AnnaStrungaru, NicolaeTcaciuc, Adi2020-04-272022-05-312022-05-312022Klick, A., Strungaru, N., & Tcaciuc, A. (2022). On arithmetic progressions in model sets. Discrete & Computational Geometry, 67, 930-946. https://doi.org/10.1007/s00454-020-00252-6https://hdl.handle.net/20.500.14078/1531We establish the existence of arbitrary-length arithmetic progressions in model sets and Meyer sets in Euclidean d-space. We prove a van der Waerden-type theorem for Meyer sets. We show that subsets of Meyer sets with positive density and pure point diffraction contain arithmetic progressions of arbitrary length.509.62KBPDFenAll Rights Reservedarithmetic progressionsMeyer setsmodel setscut-and-project schemesPost-printhttps://doi.org/10.1007/s00454-020-00252-6