Refereed journal article or data article (A1)
Characterization of repetitions in Sturmian words: A new proof
List of Authors: Jarkko Peltomäki
Publisher: Elsevier B.V.
Publication year: 2015
Journal: Information Processing Letters
Journal acronym: IPL
Volume number: 115
Issue number: 11
Start page: 886
End page: 891
Number of pages: 6
ISSN: 0020-0190
DOI: http://dx.doi.org/10.1016/j.ipl.2015.05.011
URL: http://www.sciencedirect.com/science/article/pii/S0020019015000885
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.
