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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://doi.org/10.1002/3527606572
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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, 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
Mathematics, Computing and Technology
Item ID: 8221
Depositing User: Uwe Grimm
Date Deposited: 22 Jun 2007
Last Modified: 14 Jan 2016 16:37
URI: http://oro.open.ac.uk/id/eprint/8221
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