Combinatorial problems of (quasi-)crystallography
Mathematical Physics
2007-05-23 v1 Combinatorics
Metric Geometry
math.MP
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, 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.
Keywords
Cite
@article{arxiv.math-ph/0212015,
title = {Combinatorial problems of (quasi-)crystallography},
author = {Michael Baake and Uwe Grimm},
journal= {arXiv preprint arXiv:math-ph/0212015},
year = {2007}
}
Comments
12 pages, 2 PostScript figures, LaTeX using vch-book.cls