Additive and multiplicative properties of point sets based on beta-integers. (Q1401383)

Let \(\beta\) be a unitary quadratic PV number. The authors study arithmetic properties of the set of real numbers whose \(\beta\)-expansions are polynomials in \(\beta\). This study is related to model sets, Meyer sets, quasicrystals and inflation rules (i.e., morphisms of free monoids). The authors also address the case where \(\beta\) is the unitary cubic number \(1+2\cos\frac{2\pi}{7}\). Illuminating pictures illustrate this work.