2002/12/04 by Michael Baake, Uwe Grimm
Physics and Astronomy · Mathematics · #math-ph #math.CO #math.MG #math.MP #msc:05A15 #msc:52C23 #msc:11R99
published as In: Quasicrystals - Structure and Physical Properties, ed. H.-R. Trebin (Wiley-VCH, Weinheim, 2003), pp. 160-171 · 12 pages, 2 PostScript figures, LaTeX using vch-book.cls
arxiv created 2002/12/04 · arxiv updated 2009/11/30
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.