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Lattice Substitution Systems and Model Sets

Jeong-Yup Lee·Robert V. Moody
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Abstract

The paper studies ways in which the sets of a partition of a lattice in $\RR^n$ become regular model sets. The main theorem gives equivalent conditions which assure that a matrix substitution system on a lattice in $\RR^n$ gives rise to regular model sets (based on $p$-adic-like internal spaces), and hence to pure point diffractive sets. The methods developed here are used to show that the $n-$dimensional chair tiling and the sphinx tiling are pure point diffractive.

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Jeong-Yup Lee, Robert V. Moody. 2000-02-02. Lattice Substitution Systems and Model Sets. https://arxiv.org/abs/math/0002019

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