Open Access
April, 2002 On the boundary of self affine tilings generated by Pisot numbers
J. Math. Soc. Japan 54(2): 283-308 (April, 2002). DOI: 10.2969/jmsj/05420283


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.


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Shigeki AKIYAMA. "On the boundary of self affine tilings generated by Pisot numbers." J. Math. Soc. Japan 54 (2) 283 - 308, April, 2002.


Published: April, 2002
First available in Project Euclid: 9 June 2008

zbMATH: 1032.11033
MathSciNet: MR1883519
Digital Object Identifier: 10.2969/jmsj/05420283

Primary: 11A63 , 11K26
Secondary: 28A80 , 37B50 , 52C23

Keywords: Fractal , Pisot number , tiling

Rights: Copyright © 2002 Mathematical Society of Japan

Vol.54 • No. 2 • April, 2002
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