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Quasicrystalline combinatorics

Baake, Michael and Grimm, Uwe (2003). Quasicrystalline combinatorics. In: Gazeau, J.-P.; Kerner, R.; Antoine, J.-P.; Metens, S. and Thibon, J.-Y. eds. Group 24: Physical and Mathematical Aspects of Symmetries. Institute of Physics Conference Series (173). Bristol, UK: IOP Publishing Ltd, pp. 193–200.

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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 and their module counterparts. The corresponding counting functions are encapsulated in Dirichlet series generating functions, with worked out results for the square lattice and the Tuebingen triangle tiling. Finally, we discuss a novel approach to central and averaged shelling for these examples, also involving Dirichlet series.

Item Type: Book Chapter
ISBN: 0-7503-0933-4, 978-0-7503-0933-2
Extra Information: Proceedings of the 24th International Colloquium on Group Theoretical Methods in Physics, Paris
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 12350
Depositing User: Uwe Grimm
Date Deposited: 21 Nov 2008 08:48
Last Modified: 02 Dec 2010 20:15
URI: http://oro.open.ac.uk/id/eprint/12350
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