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Geometric & Functional Analysis GAFA

, Volume 6, Issue 3, pp 471–488 | Cite as

The construction of self-similar tilings

  • R. Kenyon
Article

Abstract

We give a construction of a self-similar tiling of the plane with any prescribed expansion coefficient λɛℂ (satisfying the necessary algebraic condition of being a complex Perron number).

For any integerm>1 we show that there exists a self-similar tiling with 2π/m-rotational symmetry group and expansion λ if and only if either λ or λe2π∿/m is a complex Perron number for which e2π∿/m is in ℚ[λ], respectivelyQe2πı/m].

Keywords

Expansion Coefficient Symmetry Group Algebraic Condition Perron Number Prescribe Expansion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag 1996

Authors and Affiliations

  • R. Kenyon
    • 1
  1. 1.CNRS UMR 128 Ecole Normale Supérieure de LyonLyonFrance

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