Computing modular coincidences for substitution tilings and point sets

Frettlöh, Dirk and Sing, Bernd (2007). Computing modular coincidences for substitution tilings and point sets. Discrete and Computational Geometry, 37(3) pp. 381–401.

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URL:	http://www.springerlink.com/content/1432-0444/
DOI (Digital Object Identifier) Link:	http://dx.doi.org/10.1007/s00454-006-1280-9

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Abstract

Computing modular coincidences can show whether a given substitution system, which is supported on a point lattice in $R\!\!\!\! R^d$ , consists of model sets or not. We prove the computatibility of this problem and determine an upper bound for the number of iterations needed. The main tool is a simple algorithm for computing modular coincidences, which is essentially a generalization of the Dekking coincidence to more than one dimension, and the proof of equivalence of this generalized Dekking coincidence and modular coincidence. As a consequence, we also obtain some conditions for the existence of modular coincidences. In a separate section, and throughout the article, a number of examples are given.

Item Type:	Journal Article
ISSN:	0179-5376
Extra Information:	Article includes 11 figures. The original publication is available at www.springerlink.com. Some of the symbols may not have transferred correctly into this bibliographic record and/or abstract.
Keywords:	model sets; lattice substitution systems; coincidences
Academic Unit/Department:	Mathematics, Computing and Technology > Mathematics and Statistics
Item ID:	7503
Depositing User:	Bernd Sing
Date Deposited:	26 Apr 2007
Last Modified:	06 Dec 2010 17:36
URI:	http://oro.open.ac.uk/id/eprint/7503
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