Continuously many bounded displacement non-equivalences in substitution tiling spaces

[摘要] 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. (C) 2020 Elsevier Inc. All rights reserved.

[发布日期] 2020-12-01

[关键词] Substitution tilings;Mathematical quasicrystals;Bounded displacement;Uniformly spread