m
• E

F Nous contacter

0

# Documents  11B85 | enregistrements trouvés : 11

O

P Q

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Applications of algebra to automatic sequences and pattern avoidance - Lecture 1 Bell, Jason P. | CIRM H

Post-edited

We will cover some of the more important results from commutative and noncommutative algebra as far as applications to automatic sequences, pattern avoidance, and related areas. Well give an overview of some applications of these areas to the study of automatic and regular sequences and combinatorics on words.

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Mahler's method in several variables Adamczewski, Boris | CIRM H

Post-edited

Any algebraic (resp. linear) relation over the field of rational functions with algebraic coefficients between given analytic functions leads by specialization to algebraic (resp. linear) relations over the field of algebraic numbers between the values of these functions. Number theorists have long been interested in proving results going in the other direction. Though the converse result is known to be false in general, Mahler’s method provides one of the few known instances where it essentially holds true. After the works of Nishioka, and more recently of Philippon, Faverjon and the speaker, the theory of Mahler functions in one variable is now rather well understood. In contrast, and despite the contributions of Mahler, Loxton and van der Poorten, Kubota, Masser, and Nishioka among others, the theory of Mahler functions in several variables remains much less developed. In this talk, I will discuss recent progresses concerning the case of regular singular systems, as well as possible applications of this theory. This is a joint work with Colin Faverjon. Any algebraic (resp. linear) relation over the field of rational functions with algebraic coefficients between given analytic functions leads by specialization to algebraic (resp. linear) relations over the field of algebraic numbers between the values of these functions. Number theorists have long been interested in proving results going in the other direction. Though the converse result is known to be false in general, Mahler’s method provides ...

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Exemple d'Arnoux-Yoccoz, fractal de Rauzy, problème de Novikov : brins d'une guirlande éternelle Hubert, Pascal | CIRM H

Multi angle

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Logic, decidability and numeration systems - Lecture 1 Charlier, Émilie | CIRM H

Multi angle

Computer Science;Logic and Foundations;Number Theory

The theorem of Büchi-Bruyère states that a subset of $N^d$ is $b$-recognizable if and only if it is $b$-definable. As a corollary, the first-order theory of $(N,+,V_b)$ is decidable (where $V_b(n)$ is the largest power of the base $b$ dividing $n$). This classical result is a powerful tool in order to show that many properties of $b$-automatic sequences are decidable. The first part of my lecture will be devoted to presenting this result and its applications to $b$-automatic sequences. Then I will move to $b$-regular sequences, which can be viewed as a generalization of $b$-automatic sequences to integer-valued sequences. I will explain bow first-order logic can be used to show that many enumeration problems of $b$-automatic sequences give rise to corresponding $b$-regular sequences. Finally, I will consider more general frameworks than integer bases and (try to) give a state of the art of the research in this domain. The theorem of Büchi-Bruyère states that a subset of $N^d$ is $b$-recognizable if and only if it is $b$-definable. As a corollary, the first-order theory of $(N,+,V_b)$ is decidable (where $V_b(n)$ is the largest power of the base $b$ dividing $n$). This classical result is a powerful tool in order to show that many properties of $b$-automatic sequences are decidable. The first part of my lecture will be devoted to presenting this result and its ...

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Automatic sequences Von Haeseler, Friedrich | Walter De Gruyter 2003

Ouvrage

- 191 p.
ISBN 978-3-11-015629-4

De Gruyter expositions in mathematics , 0036

Localisation : Ouvrage RdC (HAES)

théorie des nombres # série automatique # automate # langage formel # combinatoire des mots # groupe d'Heisenberg # équation de Mahler # suite de Thue-Morse

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Substitutions in dynamics, arithmetics and combinatorics Pytheas Fogg, N. ; Berthé, V. ; Ferenczi, S. ; Mauduit, Christian ; Siegel, A. | Springer 2002

Ouvrage

- 402 p.
ISBN 978-3-540-44141-0

Lecture notes in mathematics , 1794

Localisation : Collection 1er étage

combinatoire des mots # transcendance # dynamique symbolique # fractal # théorie ergodique # suite de Sturm # fraction continue # système dynamique # suite automatique

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Algebraic combinatorics on words Lothaire, M. | Cambridge University Press 2002

Ouvrage

- xiii; 504 p.
ISBN 978-0-521-18071-9

Encyclopedia of mathematics and its applications , 0090

Localisation : Collection 1er étage

combinatoire des mots # algèbre combinatoire

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Recurrence sequences Everest, Graham ; Van der Poorten, Alf ; Shparlinski, Igor ; Ward, Thomas | American Mathematical Society 2003

Ouvrage

- 318 p.
ISBN 978-0-8218-3387-2

Mathematical surveys and monographs , 0104

Localisation : Collection 1er étage

théorie des nombres # suite définie par récurrence # recurrence # suite automatique # courbe elliptique # distribution modulo 1 # nombre pseudo-alléatoire # cryptographie # somme exponentielle # automate cellulaire

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Iterated function systems and permutation representations of the cuntz algebra Bratteli, Ola ; Jorgensen, Palle E. T. | American Mathematical Society 1999

Ouvrage

ISBN 978-0-8218-0962-4

Memoirs of the american mathematical society , 0663

Localisation : Collection 1er étage

C-algébre # analyse de Fourier # espace d'Hilbert # representation des groupes

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Automatic sequences:theory, applications, generalizations Allouche, Jean-Paul ; Shallit, Jeffrey | Cambridge University Press 2003

Ouvrage

- xvi; 571 p.
ISBN 978-0-521-82332-6

Localisation : Ouvrage RdC (ALLO)

suite automatique # théorie des nombres # combinatoire des mots # automate # morphisme uniforme # langage formel

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Automatic sequences along squares and primes Drmota, Michael | CIRM

Single angle

Number Theory

Automatic sequences and their number theoretic properties have been intensively studied during the last 20 or 30 years. Since automatic sequences are quite regular (they just have linear subword complexity) they are definitely no "quasi-random" sequences. However, the situation changes drastically when one uses proper subsequences, for example the subsequence along primes or squares. It is conjectured that the resulting sequences are normal sequences which could be already proved for the Thue-Morse sequence along the subsequence of squares.
This kind of research is very challenging and was mainly motivated by the Gelfond problems for the sum-of-digits function. In particular during the last few years there was a spectacular progress due to the Fourier analytic method by Mauduit and Rivat. In this talk we survey some of these recent developments. In particular we present a new result on subsequences along primes of so-called invertible automatic sequences.
Automatic sequences and their number theoretic properties have been intensively studied during the last 20 or 30 years. Since automatic sequences are quite regular (they just have linear subword complexity) they are definitely no "quasi-random" sequences. However, the situation changes drastically when one uses proper subsequences, for example the subsequence along primes or squares. It is conjectured that the resulting sequences are normal ...

11B85

#### Filtrer

##### Langue

Titres de périodiques et e-books électroniques (Depuis le CIRM)

Ressources Electroniques

Books & Print journals

Recherche avancée

0
Z