arXiv Open Access 2021

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

Dirk Frettlöh Alexey Garber Lorenzo Sadun

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Abstrak

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].

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math.DS math.CO math.MG

Penulis (3)

Dirk Frettlöh

Alexey Garber

Lorenzo Sadun

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Frettlöh, D., Garber, A., Sadun, L. (2021). Number of bounded distance equivalence classes in hulls of repetitive Delone sets. https://arxiv.org/abs/2101.02514

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Informasi Jurnal

Tahun Terbit: 2021
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓