33 citations · 71 across the 7 of their papers we have counts for
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Averaged coordination numbers of planar aperiodic tilings
Michael Baake, Uwe Grimm
We consider averaged shelling and coordination numbers of aperiodic tilings. Shelling numbers count the vertices on radial shells around a vertex. Coordination numbers, in turn, co…
Combinatorial problems of (quasi-)crystallography
Michael Baake, Uwe Grimm
Several combinatorial problems of (quasi-)crystallography are reviewed with special emphasis on a unified approach, valid for both crystals and quasicrystals. In particular, we con…
A guide to mathematical quasicrystals
Michael Baake
This introductory survey deals with mathematical and physical properties of discrete structures such as point sets and tilings. The emphasis is on proper generalizations of concept…
The Entropy of Square-Free Words
Michael Baake, Veit Elser, Uwe Grimm
Finite alphabets of at least three letters permit the construction of square-free words of infinite length. We show that the entropy density is strictly positive and derive reasona…
Invariant Submodules and Semigroups of Self-Similarities for Fibonacci Modules
Michael Baake, Robert V. Moody
The problem of invariance and self-similarity in Z-modules is investigated. For a selection of examples relevant to quasicrystals, especially Fibonacci modules, we determine the se…
Self-Similarities and Invariant Densities for Model Sets
Michael Baake, Robert V. Moody
Model sets (also called cut and project sets) are generalizations of lattices. Here we show how the self-similarities of model sets are a natural replacement for the group of trans…