Additive and multiplicative properties of point sets based on beta-integers.
type: Item
instance of: scholarly article
title: Additive and multiplicative properties of point sets based on beta-integers.
zbMATH Open document ID: 1036.11034
DOI: 10.1016/S0304-3975(02)00503-0
author: Christiane Frougny
author: Jean Pierre Gazeau
author: Rudolf Krejcar
published in: Theoretical Computer Science
publication date: 2003-08-17T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 11K16
Mathematics Subject Classification ID: 11B85
Mathematics Subject Classification ID: 52C23
Mathematics Subject Classification ID: 11R06
Mathematics Subject Classification ID: 68R15
zbMATH DE Number: 1965385
zbMATH Keywords: Quasicrystal
zbMATH Keywords: beta-integer
zbMATH Keywords: tiling
zbMATH Keywords: quadratic PV number
zbMATH Keywords: \(\beta\)-expansions
zbMATH Keywords: Meyer sets
zbMATH Keywords: inflation rules
reviewed by: Jean-Paul Allouche
MaRDI profile type: Publication
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full work available at URL: s0304-3975(02)00503-0
OpenAlex ID: W2129447422
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description: scientific article; zbMATH DE number 1965385