Regular subdivision in \(\mathbb{Z} [\frac{1+\sqrt{5}}{2}]\)
type: Item
instance of: scholarly article
title: Regular subdivision in \(\mathbb{Z} [\frac{1+\sqrt{5}}{2}]\)
zbMATH Open document ID: 0965.11041
author: Sean Cleary
published in: Illinois Journal of Mathematics
publication date: 2000-11-05T00:00:00Z
review text: The author shows how to construct ``regular'' subdivisions for the ring \(\mathbb{Z}[ \frac{1+\sqrt{5}}{2} ]\). He relates these subdivisions to the Fibonacci tiling and to the two substitutions \(L\to LS\), \(S\to L\) and \(L\to SL\), \(S\to L\) (used inter alia to produce one-dimensional quasi-crystals in the literature in physics). A more general result for general algebraic rings is announced.
reviewed by: Jean-Paul Allouche
Mathematics Subject Classification ID: 11R04
Mathematics Subject Classification ID: 11B85
Mathematics Subject Classification ID: 05B45
Mathematics Subject Classification ID: 52C23
Mathematics Subject Classification ID: 11B39
zbMATH DE Number: 1525072
zbMATH Keywords: subdivisions in algebraic rings
zbMATH Keywords: Fibonacci tiling
zbMATH Keywords: substitutions
zbMATH Keywords: quasi-crystals
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1525072