Balancedness of Arnoux-Rauzy and Brun words
Formal Languages and Automata Theory
2013-09-02 v1 Dynamical Systems
Abstract
We study balancedness properties of words given by the Arnoux-Rauzy and Brun multi-dimensional continued fraction algorithms. We show that almost all Brun words on 3 letters and Arnoux-Rauzy words over arbitrary alphabets are finitely balanced; in particular, boundedness of the strong partial quotients implies balancedness. On the other hand, we provide examples of unbalanced Brun words on 3 letters.
Keywords
Cite
@article{arxiv.1308.6694,
title = {Balancedness of Arnoux-Rauzy and Brun words},
author = {Vincent Delecroix and Tomáš Hejda and Wolfgang Steiner},
journal= {arXiv preprint arXiv:1308.6694},
year = {2013}
}