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Number Of Bounded Distance Equivalence Classes In Hulls Of Repetitive Delone Sets, Dirk Frettlöh, Alexey Garber, Lorenzo Sadun
Number Of Bounded Distance Equivalence Classes In Hulls Of Repetitive Delone Sets, Dirk Frettlöh, Alexey Garber, Lorenzo Sadun
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
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.