Note: Note on powers in three interval exchange transformations

Authors:
Daniel Lenz;Zuzana Masáková;Edita Pelantová
Affiliations:
Mathematisches Institut, Friedrich-Schiller Universität Jena, Ernst-Abbé Platz 2, 07743 Jena, Germany;Department of Mathematics and Doppler Institute, FNSPE, Czech Technical University in Prague, Trojanova 13, 120 00 Praha 2, Czech Republic;Department of Mathematics and Doppler Institute, FNSPE, Czech Technical University in Prague, Trojanova 13, 120 00 Praha 2, Czech Republic
Venue:
Theoretical Computer Science
Year:
2011

Citing 3
Cited 0

Infinite words with linear subword complexity

Theoretical Computer Science - Conference on arithmetics and coding systems, Marseille-Luminy, June 1987
Special factors, periodicity, and an application to Sturmian words

Acta Informatica
The index of Sturmian sequences

European Journal of Combinatorics

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Abstract

We study repetitions in infinite words coding exchange of three intervals with permutation (3, 2, 1), called 3iet words. The language of such words is determined by two parameters, @e,@?. We show that finiteness of the index of 3iet words is equivalent to boundedness of the coefficients of the continued fraction of @e. In this case, we also give an upper and a lower estimate on the index of the corresponding 3iet word. Our main tool is the connection between a 3iet word with parameters @e,@? and sturmian words with slope @e.