Letters in Mathematical Physics

, Volume 87, Issue 1–2, pp 181–195 | Cite as

Repetitions in Beta-Integers

  • L’ubomíra Balková
  • Karel Klouda
  • Edita Pelantová
Article

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.

Mathematics Subject Classification (2000)

11R06 52C23 11B05 68R15 

Keywords

repetitions in words powers of factors index of infinite words beta-integers quasicrystals aperiodic structures 

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Copyright information

© Springer 2009

Authors and Affiliations

  • L’ubomíra Balková
    • 1
  • Karel Klouda
    • 1
  • Edita Pelantová
    • 1
  1. 1.Department of Mathematics, Doppler Institute, FNSPECzech Technical University in PraguePraha 2Czech Republic

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