Journal of the Mathematical Society of Japan

On the boundary of self affine tilings generated by Pisot numbers

Shigeki AKIYAMA

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Abstract

Definition and fundamentals of tilings generated by Pisot numbers are shown by arithmetic consideration. Results include the case that a Pisot number does not have a finitely expansible property, i.e. a sofic Pisot case. Especially we show that the boundary of each tile has Lebesgue measure zero under some weak condition.

Article information

Source
J. Math. Soc. Japan, Volume 54, Number 2 (2002), 283-308.

Dates
First available in Project Euclid: 9 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1213024068

Digital Object Identifier
doi:10.2969/jmsj/05420283

Mathematical Reviews number (MathSciNet)
MR1883519

Zentralblatt MATH identifier
1032.11033

Subjects
Primary: 11K26 11A63: Radix representation; digital problems {For metric results, see 11K16}
Secondary: 37B50: Multi-dimensional shifts of finite type, tiling dynamics 52C23: Quasicrystals, aperiodic tilings 28A80: Fractals [See also 37Fxx]

Keywords
Pisot number tiling fractal

Citation

AKIYAMA, Shigeki. On the boundary of self affine tilings generated by Pisot numbers. J. Math. Soc. Japan 54 (2002), no. 2, 283--308. doi:10.2969/jmsj/05420283. https://projecteuclid.org/euclid.jmsj/1213024068


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