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- W4300560135 abstract "For a (non-unit) Pisot number $beta$, several collections of tiles are associated with $beta$-numeration. This includes an aperiodic and a periodic one made of Rauzy fractals, a periodic one induced by the natural extension of the $beta$-transformation and a Euclidean one made of integral beta-tiles. We show that all these collections (except possibly the periodic translation of the central tile) are tilings if one of them is a tiling or, equivalently, the weak finiteness property (W) holds. We also obtain new results on rational numbers with purely periodic $beta$-expansions; in particular, we calculate $gamma(beta)$ for all quadratic $beta$ with $beta^2 = a beta + b$, $gcd(a,b) = 1$." @default.
- W4300560135 created "2022-10-03" @default.
- W4300560135 creator A5008100372 @default.
- W4300560135 creator A5079044708 @default.
- W4300560135 date "2013-10-04" @default.
- W4300560135 modified "2023-10-16" @default.
- W4300560135 title "Tilings for Pisot beta numeration" @default.
- W4300560135 doi "https://doi.org/10.48550/arxiv.1310.1277" @default.
- W4300560135 hasPublicationYear "2013" @default.
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