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Monatshefte für Mathematik

, Volume 187, Issue 2, pp 275–291 | Cite as

Multiple tilings associated to d-Bonacci beta-expansions

  • Tomáš HejdaEmail author
Article
  • 54 Downloads

Abstract

Let \(\beta \in (1,2)\) be a Pisot unit and consider the symmetric \(\beta \)-expansions. We give a necessary and sufficient condition for the associated Rauzy fractals to form a tiling of the contractive hyperplane. For \(\beta \) a d-Bonacci number, i.e., Pisot root of \(x^d-x^{d-1}-\dots -x-1\) we show that the Rauzy fractals form a multiple tiling with covering degree \(d-1\).

Keywords

Beta-expansions Rauzy fractals Tiling Multiple tiling 

Mathematics Subject Classification

11A63 52C23 (11R06 37B10) 

Notes

Acknowledgements

We acknowledge support by Czech Science Foundation (GAČR) grant 17-04703Y and ANR/FWF project “FAN – Fractals and Numeration” (ANR-12-IS01-0002, FWF grant I1136). We are also grateful for Sage and TikZ software which were used to prepare the Figs. [13, 15].

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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.IRIF, CNRS UMR 8243, Université Paris Diderot – Paris 7ParisFrance
  2. 2.Department of Mathematics FCEUniversity of Chemistry and Technology, PraguePragueCzechia
  3. 3.Department of Algebra FMFCharles UniversityPragueCzechia

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