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.

DOI: https://doi.org/10.1007/s00454-006-1280-9

URL: http://www.springerlink.com/content/1432-0444/

Abstract

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.

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About

• Item ORO ID
• 7503
• Item Type
• Journal Item
• 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 or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Depositing User
• Bernd Sing