Tilings of a Riemann surface and cubic Pisot numbers

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概要

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• 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.

• 広島大学の論文

著者

• Ito Shunji

  Faculty Of Business Administration Yokohama National University

• Enomoto Fumihiko

  Graduate School of Natural Science and Technology, Kanazawa University

• Ei Hiromi

  Department of Information and System engineering, Chuo Univerity

• Furukado Maki

  Department of Information and System engineering, Chuo University

• Enomoto Fumihiko

  Graduate School Of Natural Science And Technology Kanazawa University

• Ei Hiromi

  Department Of Information And System Engineering Chuo Univerity

• Furukado Maki

  Department Of Information And System Engineering Chuo University

関連論文

• Tilings of a Riemann surface and cubic Pisot numbers
• The quasi-periodic tiling of the plane and Markov subshifts

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