Number of bounded distance equivalence classes in hulls of repetitive Delone sets

Autor:	Lorenzo Sadun, Alexey Garber, Dirk Frettlöh
Jazyk:	angličtina
Rok vydání:	2021
Předmět:	Delone set finite local complexity equivalence Dynamical Systems (math.DS) Combinatorics Mathematics - Metric Geometry Hull FOS: Mathematics Discrete Mathematics and Combinatorics Uniform boundedness Equivalence relation Mathematics::Metric Geometry Mathematics - Combinatorics aperiodic order Mathematics - Dynamical Systems Equivalence (measure theory) Equivalence class Mathematics Applied Mathematics bounded distance Metric Geometry (math.MG) aperiodic tilings topological hull Bounded function Bijection Combinatorics (math.CO) Analysis
Popis:	Two Delone sets are bounded distance equivalent to each other if there is a bijection between them such that the distance of corresponding points is uniformly bounded. Bounded distance equivalence is an equivalence relation. We show that the hull of a repetitive Delone set with finite local complexity has either one equivalence class or uncountably many. A very similar result is proven in arXiv:2011.00106 [math.MG]. 13 pages
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::514901b8a1adbf53bafa0792f78e8d6d http://arxiv.org/abs/2101.02514 Zobrazit plný text záznamu