Document Zbl 1032.11033

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On the boundary of self-affine tilings generated by Pisot numbers. (English) Zbl 1032.11033

J. Math. Soc. Japan 54, No. 2, 283-308 (2002).

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.

Reviewer: Jean-Paul Allouche (Orsay)

Cited in 1 Review

Cited in 35 Documents

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

Keywords:

first numbers; tilings; zero Lebesgue measure; fractals

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