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On the boundary of self-affine tilings generated by Pisot numbers. (English) Zbl 1032.11033
The author is interested in arithmetic and tiling properties of Pisot numbers. He obtains in particular nice results for the tiles of tilings associated with Pisot numbers: provided some weak condition is satisfied, the Lebesgue measure of the boundary of these tiles is equal to zero.

MSC:
11K55 Metric theory of other algorithms and expansions; measure and Hausdorff dimension
11R06 PV-numbers and generalizations; other special algebraic numbers; Mahler measure
28A80 Fractals
37B50 Multi-dimensional shifts of finite type, tiling dynamics (MSC2010)
52C23 Quasicrystals and aperiodic tilings in discrete geometry
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