Connections between binary patterns and paperfolding
Convergents of folded continued fractions
Corrigendum : “Complexity of infinite words associated with beta-expansions”
We add a sufficient condition for validity of Propo- sition 4.10 in the paper Frougny et al. (2004). This condition is not a necessary one, it is nevertheless convenient, since anyway most of the statements in the paper Frougny et al. (2004) use it.
Corrigendum: Complexity of infinite words associated with beta-expansions
We add a sufficient condition for validity of Propo- sition 4.10 in the paper Frougny et al. (2004). This condition is not a necessary one, it is nevertheless convenient, since anyway most of the statements in the paper Frougny et al. (2004) use it.
Critères de non-automaticité et leurs applications
Diagonalization and rationalization of algebraic Laurent series
We prove a quantitative version of a result of Furstenberg [20] and Deligne [14] stating that the diagonal of a multivariate algebraic power series with coefficients in a field of positive characteristic is algebraic. As a consequence, we obtain that for every prime the reduction modulo of the diagonal of a multivariate algebraic power series with integer coefficients is an algebraic power series of degree at most and height at most , where is an effective constant that only depends on...
Digital sum moments and substitutions
Drunken man infinite words complexity
In this article, we study the complexity of drunken man infinite words. We show that these infinite words, generated by a deterministic and complete countable automaton, or equivalently generated by a substitution over a countable alphabet of constant length, have complexity functions equivalent to n(log2n)2 when n goes to infinity.
Échanges de trois d'intervalles et suites sturmiennes
On appelle échange d’intervalles l’application qui consiste à réordonner les intervalles d’une partition de suivant une permutation donnée. Dans le cas des partitions en trois intervalles, nous donnons une caractérisation combinatoire des suites codant, d’après la partition définissant l’échange, l’orbite d’un point de sous l’action de cette transformation.
Effective polynomial upper bounds to perigees and numbers of (3x+d)-cycles of a given oddlength
Factors of generalized Rudin-Shapiro sequences. (Facteurs des suites de Rudin-Shapiro généralisées.)
Finite automata and algebraic extensions of function fields
We give an automata-theoretic description of the algebraic closure of the rational function field over a finite field , generalizing a result of Christol. The description occurs within the Hahn-Mal’cev-Neumann field of “generalized power series” over . In passing, we obtain a characterization of well-ordered sets of rational numbers whose base expansions are generated by a finite automaton, and exhibit some techniques for computing in the algebraic closure; these include an adaptation to positive...
Finite automata and arithmetic.
Fonctions digitales le long des nombres premiers
In a recent work we gave some estimations for exponential sums of the form , where Λ denotes the von Mangoldt function, f a digital function, and β a real parameter. The aim of this work is to show how these results can be used to study the statistical properties of digital functions along prime numbers.
Formules sommatoires et systèmes de numération liés aux substitutions
Frontière du fractal de Rauzy et système de numération complexe
Generalized Rudin-Shapiro sequences
Geometric realizations of substitutions
Hankel determinants for the Fibonacci word and Padé approximation
Hankel determinants of the Thue-Morse sequence
Let be the Thue-Morse sequence, i.e., the sequence defined by the recurrence equations:We consider , the double sequence of Hankel determinants (modulo 2) associated with the Thue-Morse sequence. Together with three other sequences, it obeys a set of sixteen recurrence equations. It is shown to be automatic. Applications are given, namely to combinatorial properties of the Thue-Morse sequence and to the existence of certain Padé approximants of the power series .