9 papers
Positionality of Dumont--Thomas numeration systems for integers
Savinien Kreczman, Sébastien Labbé, Manon Stipulanti
Introduced in 2001 by Lecomte and Rigo, abstract numeration systems provide a way of expressing natural numbers with words from a language accepted by a finite automaton. As it…
Symbols frequencies in the Thue--Morse word in base and related conjectures
Julien Cassaigne, Bastià n Espinoza, Michel Rigo +1
We study a binary Thue--Morse-type sequence arising from the base- expansion of integers, an archetypal automatic sequence in a rational base numeration system. Because the se…
Factor-balancedness, linear recurrence, and factor complexity
Bastià n 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…
The reflection complexity of sequences over finite alphabets
Jean-Paul Allouche, John M. Campbell, Shuo Li +2
In combinatorics on words, the well-studied factor complexity function $Ï_{\infw{x}}$ of a sequence $\infw{x}$ over a finite alphabet counts, for every nonnegative integer , th…
Doubling modulo odd integers, generalizations, and unexpected occurrences
Jean-Paul Allouche, Manon Stipulanti, Jia-Yan Yao
The starting point of this work is an equality between two quantities and found in the literature, which involve the {\em doubling-modulo-an-odd-integer} map, i.e., $x\in {…
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…