Continuously many bounded displacement non-equivalences in substitution tiling spaces
Metric Geometry
2020-04-20 v2 Combinatorics
Dynamical Systems
Abstract
We consider substitution tilings in R^d 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.
Keywords
Cite
@article{arxiv.2004.07387,
title = {Continuously many bounded displacement non-equivalences in substitution tiling spaces},
author = {Yaar Solomon},
journal= {arXiv preprint arXiv:2004.07387},
year = {2020}
}