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Balancedness of Arnoux-Rauzy and Brun words (1308.6694v1)
Published 30 Aug 2013 in cs.FL and math.DS
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.