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
Contributor : Anne Siegel
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Submitted on : Thursday, October 18, 2007 - 1:50:16 PM
Last modification on : Friday, November 16, 2018 - 1:23:22 AM
Long-term archiving on : Sunday, April 11, 2010 - 11:13:26 PM
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⟩
