Frettlöh, Dirk and Sing, Bernd
Computing modular coincidences for substitution tilings and point sets.
Discrete and Computational Geometry, 37(3) pp. 381–401.
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Computing modular coincidences can show whether a given substitution system, which is supported on a point lattice in , 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.
||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.
||model sets; lattice substitution systems; coincidences
||Mathematics, Computing and Technology > Mathematics and Statistics
||26 Apr 2007
||06 Dec 2010 17:36
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