# Boundary of central tiles associated with Pisot beta-numeration and purely periodic expansions

3 ARITH - Arithmétique informatique
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
4 SYMBIOSE - Biological systems and models, bioinformatics and sequences
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, Inria Rennes – Bretagne Atlantique
Abstract : This paper studies tilings related to the $\beta$-transformation when $\beta$ is a Pisot number (that is not supposed to be a unit). Then it applies the obtained results to study the set of rational numbers having a purely periodic $\beta$-expansion. Secial focus is given to some quadratic examples.
Document type :
Reports

Cited literature [13 references]

https://hal.inria.fr/inria-00180239
Contributor : Anne Siegel <>
Submitted on : Thursday, October 18, 2007 - 1:50:16 PM
Last modification on : Friday, November 16, 2018 - 1:23:22 AM
Document(s) archivé(s) le : Sunday, April 11, 2010 - 11:13:26 PM

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• HAL Id : inria-00180239, version 1

### Citation

Shigeki Akiyama, Guy Barat, Valerie Berthe, Anne Siegel. Boundary of central tiles associated with Pisot beta-numeration and purely periodic expansions. [Research Report] 2007. ⟨inria-00180239⟩

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