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Repetitions in Beta-Integers

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Abstract

Classical crystals are solid materials containing arbitrarily long periodic repetitions of a single motif. In this Letter, we study the maximal possible repetition of the same motif occurring in β-integers—one dimensional models of quasicrystals. We are interested in β-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 β-integers. We will solve a particular case for β being a quadratic non-simple Parry number.

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Authors and Affiliations

  1. Department of Mathematics, Doppler Institute, FNSPE, Czech Technical University in Prague, Trojanova 13, 120 00, Praha 2, Czech Republic

    L’ubomíra Balková, Karel Klouda & Edita Pelantová

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  1. L’ubomíra Balková
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  2. Karel Klouda
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  3. Edita Pelantová
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Correspondence to L’ubomíra Balková.

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Balková, L., Klouda, K. & Pelantová, E. Repetitions in Beta-Integers. Lett Math Phys 87, 181–195 (2009). https://doi.org/10.1007/s11005-009-0301-z

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  • DOI: https://doi.org/10.1007/s11005-009-0301-z

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