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.
https://hal.inria.fr/inria-00180239
Contributeur : Anne Siegel
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Soumis le : jeudi 18 octobre 2007 - 13:50:16
Dernière modification le : jeudi 24 mai 2018 - 15:59:21
Document(s) archivé(s) le : dimanche 11 avril 2010 - 23:13:26
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〉
