56 citations · 231 across the 19 of their papers we have counts for
6 papers · 1 filter
The carry propagation of the successor function
Valérie Berthé, Christiane Frougny, Michel Rigo +1
Given any numeration system, we call carry propagation at a number the number of digits that are changed when going from the representation of to the one of , and amor…
Return words of linear involutions and fundamental groups
Valérie Berthé, Vincent Delecroix, Francesco Dolce +3
We investigate the natural codings of linear involutions. We deduce from the geometric representation of linear involutions as Poincaré maps of measured foliations a suitable defin…
Maximal bifix decoding
Valérie Berthé, Clelia De Felice, Francesco Dolce +4
We introduce a class of sets of words which is a natural common generalization of Sturmian sets and of interval exchange sets. This class of sets consists of the uniformly recurren…
Acyclic, connected and tree sets
Valerie Berthé, Clelia De Felice, Francesco Dolce +4
Given a set of words, one associates to each word in an undirected graph, called its extension graph, and which describes the possible extensions of on the left and…
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…