Continuously many bounded displacement non-equivalences in substitution tiling spaces

DOI10.1016/j.jmaa.2020.124426zbMath1462.52036arXiv2004.07387OpenAlexW3044799232MaRDI QIDQ2657685

Yaar Solomon

Publication date: 14 March 2021

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.07387

zbMATH Keywords

substitution tilingsmathematical quasicrystalsbounded displacementuniformly spread

Mathematics Subject Classification ID

Quasicrystals and aperiodic tilings in discrete geometry (52C23)

Related Items (3)

A dichotomy for bounded displacement equivalence of Delone sets ⋮ On a planar six-neighbor theorem and its application ⋮ Number of bounded distance equivalence classes in hulls of repetitive Delone sets

Cites Work

• Constructing bounded remainder sets and cut-and-project sets which are bounded distance to lattices. II.
• Substitution tilings and separated nets with similarities to the integer lattice
• The family of bi-Lipschitz classes of Delone sets in Euclidean space has the cardinality of the continuum
• Substitution dynamical systems - spectral analysis
• Pisot substitution sequences, one dimensional cut-and-project sets and bounded remainder sets with fractal boundary
• A simple condition for bounded displacement
• Linearly repetitive Delone sets are rectifiable
• Constructing bounded remainder sets and cut-and-project sets which are bounded distance to lattices
• Equivalence relations on separated nets arising from linear toral flows
• Bounded interpolations between lattices
• Uniformly Spread Discrete Sets in R ^d
• Automaticity, goals, and environmental interactions.
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