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Balancedness of Arnoux-Rauzy and Brun words

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.
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https://hal.archives-ouvertes.fr/hal-00855961
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Submitted on : Friday, August 30, 2013 - 11:37:25 AM
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Vincent Delecroix, Tomáš Hejda, Wolfgang Steiner. Balancedness of Arnoux-Rauzy and Brun words. 9th International Conference, WORDS 2013, Sep 2013, Turku, Finland. pp.119-131, ⟨10.1007/978-3-642-40579-2_14⟩. ⟨hal-00855961⟩

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