Cut and project sets with polytopal window II: linear repetitivity
Cut and project sets with polytopal window II: linear repetitivity
复制标题
使用多面窗口 II 剪切和投影集：线性重复性
DOI：
10.1090/tran/8633
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发表时间：
2022
影响因子：
1.3
通讯作者：
Koivusalo H
中科院分区：
文献类型：
--
作者：
Koivusalo H
本文给出了满足弱齐性条件的凸多面体窗口切割方案和投影方案的线性重复性的完全刻画。这回答了Lagarias和Pleasants从90年代开始提出的关于切割和投影方案的自然类的问题，该类方案足够大，足以涵盖文献中感兴趣的几乎所有这样的多面体方案。我们证明了当它具有最低的面片复杂度并且满足丢番图条件时，这类切割和投影方案恰好具有线性重复性。找到正确的丢番图条件是这项工作的主要部分。为此，我们发展了一个理论，由Forrest，Hunton和Kellendonk首创，将多面体切割和投影方案分解为因素。我们还在各种各样的例子上证明了我们的主要定理，涵盖了典型切割和投影方案的所有经典例子，例如PenRose和Ammann-Beenker瓦片。参考文献
In this paper we give a complete characterisation of linear repetitivity for cut and project schemes with convex polytopal windows satisfying a weak homogeneity condition. This answers a question of Lagarias and Pleasants from the 90s for a natural class of cut and project schemes which is large enough to cover almost all such polytopal schemes which are of interest in the literature. We show that a cut and project scheme in this class has linear repetitivity exactly when it has the lowest possible patch complexity and satisfies a Diophantine condition. Finding the correct Diophantine condition is a major part of the work. To this end we develop a theory, initiated by Forrest, Hunton and Kellendonk, of decomposing polytopal cut and project schemes to factors. We also demonstrate our main theorem on a wide variety of examples, covering all classical examples of canonical cut and project schemes, such as Penrose and Ammann–Beenker tilings. References