A Simple Condition for Bounded Displacement

2011/11/07 by Yaar Solomon, Solomon, Yaar · 1 citation
Computer Science · Materials Science · #Cellular Automata and Applications #Dynamical Systems (math.DS) #FOS: Mathematics #Phase-change materials and chalcogenides #Quasicrystal Structures and Properties

paper · pdf · doi:10.48550/arxiv.1111.1690

openalex publication_date 2011/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study separated nets that correspond to substitution tilings of the Euclidean space. We give a simple condition, in terms of the eigenvalues and eigenspaces of the substitution matrix, to know whether the separated net is a bounded displacement of the integer lattice or not.

Cited by

• An exceptional set of uniformly spread Kakutani tilings of the line

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• Continuously many bounded displacement non-equivalences in substitution tiling spaces
• An exceptional set of uniformly spread Kakutani tilings of the line
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