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arXiv · 1503.07744

Multiple tilings associated to d-Bonacci beta-expansions

Tomáš Hejda
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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 $d-1$.

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Tomáš Hejda. 2015-03-24. Multiple tilings associated to d-Bonacci beta-expansions. https://arxiv.org/abs/1503.07744

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