Vincent Delecroix

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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, bound-edness of the strong partial quotients implies balancedness. On the other hand, we provide(More)
We introduce specular sets. These are subsets of groups which form a natural generalization of free groups. These sets of words are an abstract generalization of the natural codings of interval exchanges and of linear involutions. We consider two important families of sets contained in specular sets: sets of return words and maximal bifix codes. For both(More)
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