论文标题
晶格有限的距离距离距离距离设置有限的局部复杂性
Lattice Bounded Distance Equivalence for 1D Delone Sets with Finite Local Complexity
论文作者
论文摘要
适当选择的PISOT-VIJAYARAGHAVAN数字的光谱代表了有限的局部复杂性的自相似Delone点集的非平凡示例，在准晶模型中必不可少。对于我们表征的二次PISOT单元，依赖于相应的计数系统中的数字，距离平均晶格的光谱。我们的方法在剪切和项目框架中解释光谱的解释。这样的结构是通过有限字母上的无限单词编码的，这使我们能够利用组合概念，例如平衡性，取代和相关的入射矩阵的频谱。
Spectra of suitably chosen Pisot-Vijayaraghavan numbers represent non-trivial examples of self-similar Delone point sets of finite local complexity, indispensable in quasicrystal modeling. For the case of quadratic Pisot units we characterize, dependingly on digits in the corresponding numeration systems, the spectra which are bounded distance to an average lattice. Our method stems in interpretation of the spectra in the frame of the cut-and-project method. Such structures are coded by an infinite word over a finite alphabet which enables us to exploit combinatorial notions such as balancedness, substitutions and the spectrum of associated incidence matrices.
