English

Characterization of repetitions in Sturmian words: A new proof

Discrete Mathematics 2015-07-17 v2

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.

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Cite

@article{arxiv.1411.5474,
  title  = {Characterization of repetitions in Sturmian words: A new proof},
  author = {Jarkko Peltomäki},
  journal= {arXiv preprint arXiv:1411.5474},
  year   = {2015}
}

Comments

9 pages, 1 figure