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July 2007 Tilings of a Riemann surface and cubic Pisot numbers
Fumihiko Enomoto, Hiromi Ei, Maki Furukado, Shunji Ito
Hiroshima Math. J. 37(2): 181-210 (July 2007). DOI: 10.32917/hmj/1187916318

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.

Citation

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Fumihiko Enomoto. Hiromi Ei. Maki Furukado. Shunji Ito. "Tilings of a Riemann surface and cubic Pisot numbers." Hiroshima Math. J. 37 (2) 181 - 210, July 2007. https://doi.org/10.32917/hmj/1187916318

Information

Published: July 2007
First available in Project Euclid: 24 August 2007

zbMATH: 1154.53026
MathSciNet: MR2345367
Digital Object Identifier: 10.32917/hmj/1187916318

Subjects:
Primary: 37A45, 52C23
Secondary: 28A80

Rights: Copyright © 2007 Hiroshima University, Mathematics Program

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Vol.37 • No. 2 • July 2007
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