Multiple tilings associated to \(d\)-Bonacci beta-expansions. (English) Zbl 1445.11005
Summary: 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 \(d-1\).
MSC:
| 11A63 | Radix representation; digital problems |
| 11R06 | PV-numbers and generalizations; other special algebraic numbers; Mahler measure |
| 37B10 | Symbolic dynamics |
| 52C23 | Quasicrystals and aperiodic tilings in discrete geometry |
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