The Open UniversitySkip to content
 

Combinatorial problems of (quasi-)crystallography

Baake, Michael and Grimm, Uwe (2003). Combinatorial problems of (quasi-)crystallography. In: Trebin, Hans-Rainer ed. Quasicrystals: Structure and Physical Properties. Weinheim: Wiley-VCH, pp. 160–171.

URL: http://uk.arxiv.org/abs/math-ph/0212015v1
DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1002/3527606572
Google Scholar: Look up in Google Scholar

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.

Item Type: Book Chapter
ISBN: 3-527-40399-X, 978-3-527-40399-8
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 8221
Depositing User: Uwe Grimm
Date Deposited: 22 Jun 2007
Last Modified: 02 Dec 2010 20:00
URI: http://oro.open.ac.uk/id/eprint/8221
Share this page:

Actions (login may be required)

View Item
Report issue / request change

Policies | Disclaimer

© The Open University   + 44 (0)870 333 4340   general-enquiries@open.ac.uk