Some Properties of Lattice Substitution Systems

Details Some Properties of Lattice Substitution Systems Some Properties of Lattice Substitution Systems

2003-11-05

arxiv.org/abs/math/0311061v1

Mathematics

Metric Geometry

18 pages, 4 figures

Scientific paper

If a partition of a lattice in R^d is selfsimilar, it is called lattice substitution system (LSS). Such sets represent nonperiodic, but highly ordered structures. An important property of such structures is, whether they are model sets or not (equivalently, whether they are pure point diffractive or not). In this paper two conditions are given, which can be used to show that a given lattice substitution system does not consist of model sets.

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