Tilings of a Riemann surface and cubic Pisot numbers

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Author(s)

    • Ei Hiromi
    • Department of Information and System engineering, Chuo Univerity
    • Furukado Maki
    • Department of Information and System engineering, Chuo University
    • Ito Shunji
    • Faculty of Business Administration, Yokohama National University

Abstract

Using the reducible algebraic polynomial\(x^{5} - x^{4}-1 = \left( x^{2}-x + 1 \right) \left( x^{3} - x - 1 \right),\) we study two types of tiling substitutions $\tau^*$ and $\sigma^*$: $\tau^*$ generates a tiling of a plane based on five prototiles of polygons, and $\sigma^*$ generates a tiling of a Riemann surface, which consists of two copies of the plane, based on ten prototiles of parallelograms. Finally we claim that $\tau^*$-tiling of $\mathcal{P}$ equals a re-tiling of $\sigma^*$-tiling of $\mathcal{R}$ through the canonical projection of the Riemann surface to the plane.

Journal

  • Hiroshima mathematical journal

    Hiroshima mathematical journal 37(2), 181-210, 2007-07

    Hiroshima University

Codes

  • NII Article ID (NAID)
    110006311484
  • NII NACSIS-CAT ID (NCID)
    AA00664323
  • Text Lang
    ENG
  • ISSN
    00182079
  • Data Source
    NII-ELS 
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