A1 Refereed original research article in a scientific journal

Characterization of repetitions in Sturmian words: A new proof



Authors: Jarkko Peltomäki

Publisher: Elsevier B.V.

Publication year: 2015

Journal: Information Processing Letters

Journal acronym: IPL

Volume: 115

Issue: 11

First page : 886

Last page: 891

Number of pages: 6

ISSN: 0020-0190

DOI: https://doi.org/10.1016/j.ipl.2015.05.011

Web address : http://www.sciencedirect.com/science/article/pii/S0020019015000885


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.




Last updated on 2024-26-11 at 16:46