具有无限局部复杂性和 n 折旋转对称性的平顶，n=13,17,21

arXiv - MATH - Metric Geometry Pub Date : 2024-08-30 DOI:arxiv-2408.17082

April Lynne D. Say-awen

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引用次数: 0

摘要

如果一个瓦片包含无限多的双瓦片补丁，直到刚性运动为止，那么这个瓦片就被称为具有无限局部复杂性（ILC）。在这项工作中，我们提供了生成具有 ILC 的平铺的置换规则实例。除了 ILC 之外，每个替换规则的平铺空间还包含具有全局 n 倍旋转对称性（n=13,17,21）的平铺。

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Tilings with Infinite Local Complexity and n-Fold Rotational Symmetry, n=13,17,21

A tiling is said to have infinite local complexity (ILC) if it contains infinitely many two-tile patches up to rigid motions. In this work, we provide examples of substitution rules that generate tilings with ILC. The proof relies on Danzer's algorithm, which assumes that the substitution factor is non-Pisot. In addition to ILC, the tiling space of each substitution rule contains a tiling that exhibits global n-fold rotational symmetry, n=13,17,21.

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arXiv - MATH - Metric Geometry

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