Optimal embedding of Meyer sets into model sets

TL;DR

This paper provides a constructive method to embed repetitive Meyer multiple sets in Euclidean space into the smallest possible model multiple set that contains them, enhancing understanding of their structure.

Contribution

It introduces a constructive proof demonstrating that any repetitive Meyer multiple set can be embedded into a minimal model multiple set in Euclidean space.

Findings

Existence of smallest model multiple set containing a given Meyer set

Constructive method for embedding Meyer sets into model sets

Enhanced understanding of Meyer set structure and embeddings

Abstract

We give a constructive proof that a repetitive Meyer multiple set of $\mathbb{R}^d$ admits a smallest model multiple set containing it colorwise.