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Mathematics of Computation

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Tiles in quasicrystals with quartic irrationality


Author: Kevin G. Hare
Journal: Math. Comp. 78 (2009), 405-420
MSC (2000): Primary 52C23
DOI: https://doi.org/10.1090/S0025-5718-08-02137-6
Published electronically: May 14, 2008
MathSciNet review: 2448713
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Abstract: In 2003, Pelantová and Twarock did research into the number of, and types of, tiles found in 1-dimensional cut and project quasicrystals associated with 7-order symmetry. In this paper we extend this to symmetries of order 9 (degree 3), as well as orders 15, 16, 20 and 24 (degree 4). Some discussion of the next case, order 11 (degree 5), is given.


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Additional Information

Kevin G. Hare
Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1
Email: kghare@math.uwaterloo.ca

DOI: https://doi.org/10.1090/S0025-5718-08-02137-6
Received by editor(s): September 12, 2007
Received by editor(s) in revised form: January 10, 2008
Published electronically: May 14, 2008
Additional Notes: The research of K. G. Hare was supported, in part, by NSERC of Canada. Computational support was provided for, in part, by the Canadian Foundation for Innovation and the Ontario Research Fund.
Article copyright: © Copyright 2008 by the author