02-392 Michael Baake, Uwe Grimm

Quasicrystalline Combinatorics (120K, Postscript) Sep 19, 02

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Abstract. Several combinatorial problems of (quasi)crystallography are reviewed with special emphasis on a unified approach, valid for both crystals and quasicrystals. In particular, we consider planar sublattices, similarity sublattices, coincidence sublattices and their module counterparts. The corresponding counting functions are encapsulated in Dirichlet series generating functions, with worked out results for the square lattice and the T"ubingen triangle tiling. Finally, we discuss a novel approach to central and averaged shelling for these examples, also involving Dirichlet series.

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