56 citations · 79 across the 13 of their papers we have counts for
16 papers
On balanced sequences and their critical exponent
Francesco Dolce, Lubomira Dvorakova, Edita Pelantova
We study aperiodic balanced sequences over finite alphabets. A sequence vv of this type is fully characterised by a Sturmian sequence u and two constant gap sequences y and y'. We…
On morphisms preserving palindromic richness
Francesco Dolce, Edita Pelantová
It is known that each word of length contains at most distinct palindromes. A finite rich word is a word with maximal number of palindromic factors. The definition of pal…
Some variations on Lyndon words
Francesco Dolce, Antonio Restivo, Christophe Reutenauer
In this paper we compare two finite words and by the lexicographical order of the infinite words and . Informally, we say that we compare and by the infi…
On generalized Lyndon words
Francesco Dolce, Antonio Restivo, Christophe Reutenauer
A generalized lexicographical order on infinite words is defined by choosing for each position a total order on the alphabet. This allows to define generalized Lyndon words. Every…
Eventually dendric subshifts
Francesco Dolce, Dominique Perrin
We define a new class of shift spaces which contains a number of classes of interest, like Sturmian shifts used in discrete geometry. We show that this class is closed under two na…
Birecurrent sets
Francesco Dolce, Dominique Perrin, Antonio Restivo +2
A set is called recurrent if its minimal automaton is strongly connected and birecurrent if it is recurrent as well as its reversal. We prove a series of results concerning birecur…
Specular sets
Valérie Berthé, Clelia De Felice, Vincent Delecroix +5
We introduce the notion of specular sets which are subsets of groups called here specular and which form a natural generalization of free groups. These sets are an abstract general…
Enumeration formulæ in neutral sets
Francesco Dolce, Dominique Perrin
We present several enumeration results holding in sets of words called neutral and which satisfy restrictive conditions on the set of possible extensions of nonempty words. These f…
Bifix codes and interval exchanges
Valérie Berthé, Clelia De Felice, Francesco Dolce +4
We investigate the relation between bifix codes and interval exchange transformations. We prove that the class of natural codings of regular interval echange transformations is clo…
Regular Interval Exchange Transformations over a Quadratic Field
Francesco Dolce
We describe a generalization of a result of Boshernitzan and Carroll: an extension of Lagrange's Theorem on continued fraction expansion of quadratic irrationals to interval exchan…
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…
Notes on sets of first return
Valérie Berthé, Clelia De Felice, Francesco Dolce +3
We prove in this note that, for an alphabet with three letters, the set of first return to a given word in a set satisfying the tree condition is a basis of the free group.
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…
The finite index basis property
Valérie Berthé, Clelia De Felice, Francesco Dolce +4
We describe in this paper a connection between bifix codes, symbolic dynamical systems and free groups. This is in the spirit of the connection established previously for the symbo…
Interval exchanges, admissibility and branching Rauzy induction
Francesco Dolce, Dominique Perrin
We introduce a definition of admissibility for subintervals in interval exchange transformations. Using this notion, we prove a property of the natural codings of interval exchange…