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We study balancedness properties of words given by the Arnoux-Rauzy and Brunmulti-dimensional continued fraction algorithms. We show that almost all Brunwords on 3 letters and Arnoux-Rauzy words over arbitrary alphabets are finitelybalanced; in particular, boundedness of the strong partial quotients impliesbalancedness. On the other hand, we provide examples of unbalanced Brun wordson 3 letters.

Balancedness of Arnoux-Rauzy and Brun words