Continuously many bounded displacement non-equivalences in substitution tiling spaces

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2 Scopus citations

Abstract

We consider substitution tilings in Rd that give rise to point sets that are not bounded displacement (BD) equivalent to a lattice and study the cardinality of BD(X), the set of distinct BD class representatives in the corresponding tiling space X. We prove a sufficient condition under which the tiling space contains continuously many distinct BD classes and present such an example in the plane. In particular, we show here for the first time that this cardinality can be greater than one.

Original languageEnglish
Article number124426
JournalJournal of Mathematical Analysis and Applications
Volume492
Issue number1
DOIs
StatePublished - 1 Dec 2020

Keywords

  • Bounded displacement
  • Mathematical quasicrystals
  • Substitution tilings
  • Uniformly spread

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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