56 citations · 231 across the 19 of their papers we have counts for
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Uniformly balanced words with linear complexity and prescribed letter frequencies
Valérie Berthé, Sébastien Labbé
We consider the following problem. Let us fix a finite alphabet A; for any given d-uple of letter frequencies, how to construct an infinite word u over the alphabet A satisfying th…
Substitutive Arnoux-Rauzy sequences have pure discrete spectrum
Valérie Berthé, Timo Jolivet, Anne Siegel
We prove that the symbolic dynamical system generated by a purely substitutive Arnoux-Rauzy sequence is measurably conjugate to a toral translation. The proof is based on an explic…
Selfdual Substitutions in Dimension One
Valérie Berthé, Dirk Frettlöh, Victor Sirvent
There are several notions of the 'dual' of a word/tile substitution. We show that the most common ones are equivalent for substitutions in dimension one, where we restrict ourselve…
Connectedness of fractals associated with Arnoux-Rauzy substitutions
Valérie Berthé, Timo Jolivet, Anne Siegel
Rauzy fractals are compact sets with fractal boundary that can be associated with any unimodular Pisot irreducible substitution. These fractals can be defined as the Hausdorff limi…