Balancedness of Arnoux-Rauzy and Brun words
Vincent Delecroix, Tomáš Hejda, Wolfgang Steiner · 2013
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. 1