Combinatorial problems of (quasi-)crystallography

Details Combinatorial problems of (quasi-)crystallography Combinatorial problems of (quasi-)crystallography

2002-12-04

arxiv.org/abs/math-ph/0212015v1

In: Quasicrystals - Structure and Physical Properties, ed. H.-R. Trebin (Wiley-VCH, Weinheim, 2003), pp. 160-171

Physics

Mathematical Physics

12 pages, 2 PostScript figures, LaTeX using vch-book.cls

Scientific paper

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, their module counterparts, and central and averaged shelling. The corresponding counting functions are encapsulated in Dirichlet series generating functions, with explicit results for the triangular lattice and the twelvefold symmetric shield tiling. Other combinatorial properties are briefly summarised.

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