数学准晶体指南
A guide to mathematical quasicrystals
摘要：
这个介绍性的调查涉及离散结构，如点集和平铺的数学和物理特性。重点是从经典晶体学的概念和思想的适当概括。特别是，我们专注于他们的相互作用与各种物理动机的等价概念，如本地不可分割性和本地等价。详细描述了具有非晶体学对称性的各种离散图案，并介绍了它们的一些神奇性质。这个完美有序的世界是通过对随机平铺的随机世界的简要介绍来增强的。
英文摘要：
This introductory survey deals with mathematical and physical properties of discrete structures such as point sets and tilings. The emphasis is on proper generalizations of concepts and ideas from classical crystallography. In particular, we focus on their interplay with various physically motivated equivalence concepts such as local indistinguishability and local equivalence. Various discrete patterns with non-crystallographic symmetries are described in detail, and some of their magic properties are introduced. This perfectly ordered world is augmented by a brief introduction to the stochastic world of random tilings.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
