Year: 2026
Type: preprint
Abstract: We consider Delone point patterns with self-similarity. Under mild conditions, the similarity factor is a Pisot number if and only if the pattern is uniformly discrete. The classical case is a Meyer set $Λ$ with $Λ\supset θΛ$ for some $θ>1,$ for which $θ$ must be a Pisot number or a Salem number. When $Λ$ contains several similar copies of itself, the case of a Salem number drops out for $θ<2.$ On the other hand, strictly self-similar patterns with a Pisot factor must be Meyer sets. Various examples are given.
Source: arXiv (Cornell University)
Authors: Bandt, Christoph, Meyer, Yves
Subfield: Materials Chemistry
Field: Materials Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7202397015
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