Multiple tilings associated to d-Bonacci beta-expansions

Abstract

Let ss. (1, 2) be a Pisot unit and consider the symmetric ss-expansions. We give a necessary and sufficient condition for the associated Rauzy fractals to form a tiling of the contractive hyperplane.

For ss a d-Bonacci number, i. e., Pisot root of xd -xd-1 center dot center dot center dot -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