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Characterization of Repetitions in Sturmian Words: A New Proof

Jarkko Peltomäki, Characterization of Repetitions in Sturmian Words: A New Proof. Information Processing Letters 115(11), 886–891, 2015.

http://dx.doi.org/10.1016/j.ipl.2015.05.011

Abstract:

We present a new, dynamical way to study powers (that is, repetitions) in Sturmian words based on results from Diophantine approximation theory. As a result, we provide an alternative and shorter proof of a result by Damanik and Lenz characterizing powers in Sturmian words [Powers in Sturmian Sequences, Eur. J. Combin. 24 (2003), 377–390]. Further, as a consequence, we obtain a previously known formula for the fractional index of a Sturmian word based on the continued fraction expansion of its slope.

BibTeX entry:

@ARTICLE{jPeltomaki_Jarkko15a,
  title = {Characterization of Repetitions in Sturmian Words: A New Proof},
  author = {Peltomäki, Jarkko},
  journal = {Information Processing Letters},
  volume = {115},
  number = {11},
  publisher = {Elsevier},
  pages = {886–891},
  year = {2015},
  keywords = {formal languages,sturmian word,standard word,power,continued fraction},
  ISSN = {0020-0190},
}

Belongs to TUCS Research Unit(s): FUNDIM, Fundamentals of Computing and Discrete Mathematics

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