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arXiv · 0812.4006

Repetitions in beta-integers

L. Balková·K. Klouda·E. Pelantová
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Abstract

Classical crystals are solid materials containing arbitrarily long periodic repetitions of a single motif. In this paper, we study the maximal possible repetition of the same motif occurring in beta-integers -- one dimensional models of quasicrystals. We are interested in beta-integers realizing only a finite number of distinct distances between neighboring elements. In such a case, the problem may be reformulated in terms of combinatorics on words as a study of the index of infinite words coding beta-integers. We will solve a particular case for beta being a quadratic non-simple Parry number.

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L. Balková, K. Klouda, E. Pelantová. 2008-12-21. Repetitions in beta-integers. https://doi.org/10.1007/s11005-009-0301-z

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