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Kolakoski-(3, 1) Is a (Deformed) Model Set

Published online by Cambridge University Press:  20 November 2018

Michael Baake  and
Bernd Sing
Bernd Sing
Affiliation:
Institut für Mathematik Universität Greifswald Jahnstr. 15a 17487 Greifswald Germany, e-mail: sing@uni-greifswald.de, http://schubert.math-inf.uni-greifswald.de
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Abstract

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Unlike the (classical) Kolakoski sequence on the alphabet {1, 2}, its analogue on {1, 3} can be related to a primitive substitution rule. Using this connection, we prove that the corresponding bi-infinite fixed point is a regular generic model set and thus has a pure point diffraction spectrum. The Kolakoski-(3, 1) sequence is then obtained as a deformation, without losing the pure point diffraction property.

Keywords

52C2337B1028A8043A25
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 47 , Issue 2 , 01 June 2004 , pp. 168 - 190
Copyright
Copyright © Canadian Mathematical Society 2004

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