14 citations · 33 across the 30 of their papers we have counts for
21 papers · 1 filter
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…
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…
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…
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-…
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…
Regular sequences and synchronized sequences in abstract numeration systems
Émilie Charlier, Célia Cisternino, Manon Stipulanti
The notion of -regular sequences was generalized to abstract numeration systems by Maes and Rigo in 2002. Their definition is based on a notion of -kernel that exte…
Robustness of Pisot-regular sequences
Émilie Charlier, Célia Cisternino, Manon Stipulanti
We consider numeration systems based on a -tuple of sequences of integers and we define -regular sequences through $\mathb…
Avoiding 5/4-powers on the alphabet of nonnegative integers
Eric Rowland, Manon Stipulanti
We identify the structure of the lexicographically least word avoiding 5/4-powers on the alphabet of nonnegative integers. Specifically, we show that this word has the form $p τ(φ(…
The Formal Inverse of the Period-Doubling Sequence
Narad Rampersad, Manon Stipulanti
If is a prime number, consider a -automatic sequence , and let be its generating function. Assume that t…
Nyldon words
Émilie Charlier, Manon Philibert, Manon Stipulanti
The Chen-Fox-Lyndon theorem states that every finite word over a fixed alphabet can be uniquely factorized as a lexicographically nonincreasing sequence of Lyndon words. This theor…
Convergence of Pascal-Like Triangles in Parry-Bertrand Numeration Systems
Manon Stipulanti
We pursue the investigation of generalizations of the Pascal triangle based on binomial coefficients of finite words. These coefficients count the number of times a finite word app…
Counting Subwords Occurrences in Base-b Expansions
Julien Leroy, Michel Rigo, Manon Stipulanti
We count the number of distinct (scattered) subwords occurring in the base-b expansion of the non-negative integers. More precisely, we consider the sequence co…
Counting the number of non-zero coefficients in rows of generalized Pascal triangles
Julien Leroy, Michel Rigo, Manon Stipulanti
This paper is about counting the number of distinct (scattered) subwords occurring in a given word. More precisely, we consider the generalization of the Pascal triangle to binomia…
Generalized Pascal triangle for binomial coefficients of words
Julien Leroy, Michel Rigo, Manon Stipulanti
We introduce a generalization of Pascal triangle based on binomial coefficients of finite words. These coefficients count the number of times a word appears as a subsequence of ano…