7 papers
State Complexity of Shifts of the Fibonacci Word
Delaram Moradi, Pierre Popoli, Jeffrey Shallit +1
The Fibonacci infinite word is one of the most celebrated objects in combinatorics on words. There is a simple -state automaton tha…
Factor-balancedness, linear recurrence, and factor complexity
Bastiàn Espinoza, Pierre Popoli, Manon Stipulanti
In the study of infinite words, various notions of balancedness provide quantitative measures for how regularly letters or factors occur, and they find applications in several area…
Computing Expansions in Infinitely Many Cantor Real Bases via a Single Transducer
Émilie Charlier, Pierre Popoli, Michel Rigo
Representing real numbers using convenient numeration systems (integer bases, -numeration, Cantor bases, etc.) has been a longstanding mathematical challenge. This paper focuses…
Effective Computation of Generalized Abelian Complexity for Pisot Type Substitutive Sequences
Jean-Michel Couvreur, Martin Delacourt, Nicolas Ollinger +3
Generalized abelian equivalence compares words by their factors up to a certain bounded length. The associated complexity function counts the equivalence classes for factors of a g…
Additive word complexity and Walnut
Pierre Popoli, Jeffrey Shallit, Manon Stipulanti
In combinatorics on words, a classical topic of study is the number of specific patterns appearing in infinite sequences. For instance, many works have been dedicated to studying t…
On the pseudorandomness of Parry--Bertrand automatic sequences
Pierre Popoli, Manon Stipulanti
The correlation measure is a testimony of the pseudorandomness of a sequence $\infw{s}$ and provides information about the independence of some parts of $\infw{s}$ and their shifts…
Combinatorics on Social Configurations
Dylan Laplace Mermoud, Pierre Popoli
In cooperative game theory, the social configurations of players are modeled by balanced collections. The Bondareva-Shapley theorem, perhaps the most fundamental theorem in coopera…