14 citations · 33 across the 30 of their papers we have counts for
36 papers
An example of an automatic sequence with non-regular abelian complexity
Jean-Paul Allouche, Narad Rampersad, Michel Rigo +2
Answering a question of Madill and Rampersad, we give an example a of a -automatic sequence whose abelian complexity is not -regular.
Gosper's and Ramanujan's infinite products and generalizations
Jean-Paul Allouche, John M. Campbell, Simon R. Holcombe +2
Gosper introduced many remarkable formulas involving infinite products. One such formula provides an evaluation of the product $$\prod_{n \geq 1} \frac{1}{e}\left(\frac{1}{3n} + 1\…
Symbols frequencies in the Thue--Morse word in base and related conjectures
Julien Cassaigne, Bastiàn 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
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…
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…
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…
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…
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 $ρ_{\infw{x}}$ of a sequence $\infw{x}$ over a finite alphabet counts, for every nonnegative integer , the…
Automatic Abelian Complexities of Parikh-Collinear Fixed Points
Michel Rigo, Manon Stipulanti, Markus A. Whiteland
Parikh-collinear morphisms have the property that all the Parikh vectors of the images of letters are collinear, i.e., the associated adjacency matrix has rank 1. In the conference…
Exploring the Crochemore and Ziv-Lempel factorizations of some automatic sequences with the software Walnut
Marieh Jahannia, Manon Stipulanti
We explore the Ziv-Lempel and Crochemore factorizations of some classical automatic sequences making an extensive use of the theorem prover Walnut.
Combinatorics on words and generating Dirichlet series of automatic sequences
Jean-Paul Allouche, Jeffrey Shallit, Manon Stipulanti
Generating series are crucial in enumerative combinatorics, analytic combinatorics, and combinatorics on words. Though it might seem at first view that generating Dirichlet series…
Summing the sum of digits
Jean-Paul Allouche, Manon Stipulanti
We revisit and generalize inequalities for the summatory function of the sum of digits in a given integer base. We prove that several known results can be deduced from a theorem in…
An elementary proof of Bridy's theorem
Eric Rowland, Manon Stipulanti, Reem Yassawi
Christol's theorem states that a power series with coefficients in a finite field is algebraic if and only if its coefficient sequence is automatic. A natural question is how the s…
Magic numbers in periodic sequences
Savinien Kreczman, Luca Prigioniero, Eric Rowland +1
In formal languages and automata theory, the magic number problem can be formulated as follows: for a given integer n, is it possible to find a number d in the range [n,2^n] such t…
String attractors of some simple-Parry automatic sequences
France Gheeraert, Giuseppe Romana, Manon Stipulanti
Firstly studied by Kempa and Prezza in 2018 as the cement of text compression algorithms, string attractors have become a compelling object of theoretical research within the commu…
On extended boundary sequences of morphic and Sturmian words
Michel Rigo, Manon Stipulanti, Markus A. Whiteland
Generalizing the notion of the boundary sequence introduced by Chen and Wen, the th term of the -boundary sequence of an infinite word is the finite set of pairs o…
A full characterization of Bertrand numeration systems
Émilie Charlier, Célia Cisternino, Manon Stipulanti
Among all positional numeration systems, the widely studied Bertrand numeration systems are defined by a simple criterion in terms of their numeration languages. In 1989, Bertrand-…
On digital sequences associated with Pascal's triangle
Pierre Mathonet, Michel Rigo, Manon Stipulanti +1
We consider the sequence of integers whose th term has base- expansion given by the th row of Pascal's triangle modulo (where is a prime number). We first present…
Characterizations of families of morphisms and words via binomial complexities
Michel Rigo, Manon Stipulanti, Markus A. Whiteland
Two words are -binomially equivalent if each subword of length at most occurs the same number of times in both words. The -binomial complexity of an infinite word is a co…
Closed Ziv-Lempel factorization of the -bonacci words
Marieh Jahannia, Morteza Mohammad-noori, Narad Rampersad +1
A word is said to be closed if it has a proper factor which occurs exactly twice in , as a prefix and as a suffix of . Based on the concept of Ziv-Lempel factorizatio…
Revisiting regular sequences in light of rational base numeration systems
Michel Rigo, Manon Stipulanti
Regular sequences generalize the extensively studied automatic sequences. Let be an abstract numeration system. When the numeration language is prefix-closed and regular, a…
Automatic sequences: from rational bases to trees
Michel Rigo, Manon Stipulanti
The th term of an automatic sequence is the output of a deterministic finite automaton fed with the representation of in a suitable numeration system. In this paper, instead…