WorldCat Identities

Berthé, V. (Valérie) 1957-

Overview
Works: 49 works in 124 publications in 2 languages and 2,215 library holdings
Genres: Conference papers and proceedings 
Roles: Editor, Author, Opponent, Other, Thesis advisor, htt, Contributor
Publication Timeline
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Most widely held works by V Berthé
Combinatorics, automata, and number theory by V Berthé( )

20 editions published between 2008 and 2010 in English and held by 1,031 WorldCat member libraries worldwide

This collaborative volume presents recent trends arising from the fruitful interaction between combinatorics on words, automata and number theory
Substitutions in dynamics, arithmetics, and combinatorics by N Pytheas Fogg( Book )

14 editions published between 2002 and 2003 in English and held by 555 WorldCat member libraries worldwide

A certain category of infinite strings of letters on a finite alphabet is presented here, chosen among the 'simplest' possible one may build, both because they are very deterministic and because they are built by simple rules (a letter is replaced by a word, a sequence is produced by iteration). These substitutive sequences have a surprisingly rich structure. The authors describe the concepts of quantity of natural interactions, with combinatorics on words, ergodic theory, linear algebra, spectral theory, geometry of tilings, theoretical computer science, diophantine approximation, trancendence, graph theory. This volume fulfils the need for a reference on the basic definitions and theorems, as well as for a state-of-the-art survey of the more difficult and unsolved problems
Combinatorics, words and symbolic dynamics( Book )

11 editions published between 2015 and 2016 in English and held by 278 WorldCat member libraries worldwide

"Internationally recognised researchers look at developing trends in combinatorics with applications in the study of words and in symbolic dynamics. They explain the important concepts, providing a clear exposition of some recent results, and emphasise the emerging connections between these different fields. Topics include combinatorics on words, pattern avoidance, graph theory, tilings and theory of computation, multidimensional subshifts, discrete dynamical systems, ergodic theory, numeration systems, dynamical arithmetics, automata theory and synchronised words, analytic combinatorics, continued fractions and probabilistic models. Each topic is presented in a way that links it to the main themes, but then they are also extended to repetitions in words, similarity relations, cellular automata, friezes and Dynkin diagrams. The book will appeal to graduate students, research mathematicians and computer scientists working in combinatorics, theory of computation, number theory, symbolic dynamics, tilings and stringology. It will also interest biologists using text algorithms"--
Sequences, groups, and number theory( )

15 editions published in 2018 in English and held by 246 WorldCat member libraries worldwide

This collaborative book presents recent trends on the study of sequences, including combinatorics on words and symbolic dynamics, and new interdisciplinary links to group theory and number theory. Other chapters branch out from those areas into subfields of theoretical computer science, such as complexity theory and theory of automata. The book is built around four general themes: number theory and sequences, word combinatorics, normal numbers, and group theory. Those topics are rounded out by investigations into automatic and regular sequences, tilings and theory of computation, discrete dynamical systems, ergodic theory, numeration systems, automaton semigroups, and amenable groups. This volume is intended for use by graduate students or research mathematicians, as well as computer scientists who are working in automata theory and formal language theory. With its organization around unified themes, it would also be appropriate as a supplemental text for graduate level courses
Actes des Journées Montoises d'Informatique Théorique : 9-11 Septembre 2002, Montpellier, France by Journées Montoises d'Informatique Théorique( Book )

4 editions published in 2003 in French and English and held by 26 WorldCat member libraries worldwide

Combinatorics, Words and Symbolic Dynamics( )

3 editions published in 2015 in English and held by 9 WorldCat member libraries worldwide

Internationally recognised researchers look at developing trends in combinatorics with applications in the study of words and in symbolic dynamics. They explain the important concepts, providing a clear exposition of some recent results, and emphasise the emerging connections between these different fields. Topics include combinatorics on words, pattern avoidance, graph theory, tilings and theory of computation, multidimensional subshifts, discrete dynamical systems, ergodic theory, numeration systems, dynamical arithmetics, automata theory and synchronised words, analytic combinatorics, continued fractions and probabilistic models. Each topic is presented in a way that links it to the main themes, but then they are also extended to repetitions in words, similarity relations, cellular automata, friezes and Dynkin diagrams. The book will appeal to graduate students, research mathematicians and computer scientists working in combinatorics, theory of computation, number theory, symbolic dynamics, tilings and stringology. It will also interest biologists using text algorithms
Combinatorics by V Berthé( Book )

2 editions published in 2016 in English and held by 8 WorldCat member libraries worldwide

Combinatorics, automata and number theory( Book )

4 editions published between 2007 and 2008 in English and held by 7 WorldCat member libraries worldwide

Structure des pavages, droites discrètes 3D et combinatoire des mots by Sébastien Labbé( Book )

3 editions published in 2012 in French and held by 4 WorldCat member libraries worldwide

This thesis, consisting of a series of articles, considers issues arising in discrete geometry by treating them in terms of combinatorics of words: a powerful and appropriate tool to address them. We use words to represent either a path in S ZZA2 S or S ZZA3 S, either to encode the sequence of turns of a path or represent the boundary of a discrete closed figure. Topics covered include tilings of the plane by copies of a polyomino, the notion of palindrome complexity and generation of 3D discrete lines. The first part concerns the tilings of the plane where we study the number of regular tilings of the plane by a tile. It turns out that some polyominoes can tile the plane in two distinct ways with four tiles adjacent. They are called double square. We first demonstrate there are at most two such regular tilings by a tile. Next, we consider two particular families of double squares: Christoffel tiles and Fibonacci tiles. These two families describe the smallest examples of double squares and can be defined from the Christoffel words and the Fibonacci word by rules of substitution and concatenation. The Fibonacci tiles also define a fractal, obtained by the limit of a sequence of closed self-avoiding path, we calculated several statistics including the ratio of the area of the fractal on the area of its convex hull. In the next article, we demonstrate that indecomposable double squares are invariant under a rotation of 180 degrees. This geometric property is equivalent to the fact that their boundary word can be factorized into a product of palindromes. Our proof is based on an exhaustive method of generating double squares. The second part concerns the palindromic complexity - the number of distinct palindrome factors - a proper subject of combinatorics on words. We consider four classes of palindromic complexity arising naturally from the notion of palindromic defect. We characterize words on a two-letter alphabet having a minimal palindromic complexity and we show that the infinite words obtained by codings of rotations on two intervals reach the maximum palindromic complexity. In the third part, we propose a method based on multidimensional continued fraction algorithms for the generation of 3D discrete lines S6S-connected. Experiments illustrate that the complexity of factors in words and generated would be linear. This compares favorably with other definitions of 3D discrete S6S-connected lines whose factor complexity is quadratic. Seven articles are included in the thesis
Arithmetic distributions of convergents arising from Jacobi-Perron algorithm by V Berthé( Book )

2 editions published in 2004 in English and held by 3 WorldCat member libraries worldwide

Fonction de Carlitz et automates : entropies conditionnelles by V Berthé( Book )

2 editions published in 1994 in French and held by 3 WorldCat member libraries worldwide

CE TRAVAIL SE DIVISE EN DEUX PARTIES INDEPENDANTES. DANS LA PREMIERE, NOUS DEMONTRONS, EN UTILISANT LES AUTOMATES FINIS, DES RESULTATS DE TRANSCENDANCE DANS LE MODULE DE CARLITZ DE RANG 1. DANS LA SECONDE PARTIE, NOUS NOUS INTERESSONS A DES ENTROPIES CONDITIONNELLES DE BLOCS, AU SENS DE SHANNON, POUR DES SUITES A VALEURS DANS UN ALPHABET FINI, ET EN PARTICULIER, POUR LES SUITES STURMIENNES
Covering numbers: Arithmetics and dynamics for rotations and interval exchanges by V Berthé( )

1 edition published in 1999 in English and held by 2 WorldCat member libraries worldwide

Odometers on Regular Languages by V Berthé( )

1 edition published in 2005 in English and held by 2 WorldCat member libraries worldwide

Mots de retours et pavages dans les plans sturmiens by Matthieu Simonet( )

1 edition published in 2012 in French and held by 2 WorldCat member libraries worldwide

Sturmian words are a way to encode aperiodic discrete lines. They have been studied since the end of the 19th century and can be characterized in many ways. One of these characterizations, obtained by Vuillon, centers around the notion of return words.This thesis aims to study 2-dimensional Sturmian words as encodings of aperiodic discrete planes. It is a first step towards a characterization of 2-dimensional Sturmian words analogous to that of Vuillon in dimension 1.However, concerns specific to dimension 2, such as the impossibility to concatenate words or the difficulty to locate a factor inside a word make the study much trickier. To tackle this, we introduce in dimension 2 notions of patterns, pointed patterns, localization words and return words.We obtain a 2-dimensional version of a theorem of Morse and Hedlund concerning certain return words in a Sturmian word. This result enables us to establish a new continued-fractions algorithm and to introduce, in a restricted setting, a notion of derived sequence
Substitutions sur la droite et dans le plan by Guillaume Delalleau( Book )

2 editions published in 2011 in French and held by 2 WorldCat member libraries worldwide

This memoir is split in two parts of three chapters each. The theme of the first part is S-adic words. The first chapter is concerned with the convergence of S-adic sequences; we propose a general form for the accumulation points of S-adic sequences, and infer from it general sufficient conditions for the convergence. In the second chapter, conditions on the alphabet of substitutions for the S-adic words to form an attractor in the set of infinite words. When these conditions are met, we adumbrate a way to a solution of the S-adic conjecture. The first step, a more systematic study of the factorial complexity of fixed points of substitutions, is taken and partial results are obtained. In the third chapter, we touch upon the question of the existence of frequencies for letters in S-adic words through the action of substitutions on the frequency simplex. The second part is concerned with tilings of the plane with square and colored tiles. In the fifth chapter, we propose a representation of patches by graphs and give necessary and sufficient conditions for a graph to represent a patch. In the sixth chapter we define bidimensional substitutions as transformations of the vertices ans edges of the graph representing patches; necessary and sufficient conditions for a graph thus built to represent a patch are given. In the seventh chapter we propose a construction of S-adic tilings of the plane by square and colored tiles
Combinatoire de substitutions de type Pisot = ombinatorics of Pisot substitutions by Timothée Jolivet( Book )

2 editions published in 2013 in French and held by 2 WorldCat member libraries worldwide

Substitutions are mappings which replace each symbol of a given alphabet by a word over the same alphabet. They naturally act over infinite sequences of symbols, and produce highly ordered Systems with many properties. This thesis concerns a particular class with algebraic restrictions, Pisot substitutions, and their related objects of dynamical, fractal o combinatorial nature. We begin with the combinatorial study of some qualitative properties of the two-dimensional patterns generated by iterating a two-dimensional "dual" version of Pisot substitutions. We apply these results to study the infinite families of substitutions obtained by taking arbitrary products over a finite set of Pisot substitutions. Applications include dynamica properties of the associated symbolic Systems, some language theoretical characterization of some topological properties of their associated Rauzy fractals, some number-theoretical properties of their associated Pisot numbers, and some results in discrete geometry. Particular focus is set on the substitutions associated with the Arnoux-Rauzy, Brun and Jacobi-Perron multidimensional continued fraction algorithms Next we give explicit construction to give a complete description of the possible fondamental groups of planar Rauzy fractals in the case where the group is countable. In the last two chapters, we "step back" from the Pisot algebraic assumption to study some more general objects arising from the combinatorial tools used in the previous chapters, focusing on some computational (un)decidability questions
Approche dynamique et combinatoire de la notion de discrépance by Boris Adamczewski( Book )

2 editions published in 2002 in French and held by 2 WorldCat member libraries worldwide

Boundary of central tiles associated with Pisot beta-numeration and purely periodic expansions by Shigeki Akiyama( )

1 edition published in 2008 in English and held by 2 WorldCat member libraries worldwide

Automates Cellulaires : aspects algorithmiqued des configurations périodiques en toute dimension by Nicolas Bacquey( Book )

2 editions published in 2015 in French and held by 2 WorldCat member libraries worldwide

This thesis analyses the computational capabilities of cellular automata working on periodical configurations of any dimension. We first study the maximal objects these cellular automata can identify; we call those objects primitive roots of periodical configurations of any dimension. We characterize them and show some of their properties. Secondly, we present a set of algorithms on cellular automata, each one adapted to one or more dimensions, that extract primitive roots from the periodical configurations on which they are applied. Those algorithms use original tools that extend the notion of signals on cellular automata. Beyond its technical and algorithmical aspects, this thesis lays the foundations of uniform periodical computation, i.e. computation performed on a model whose program and entry data are isotropic. In particular, we address the issues of halting such computation, reading its result and defining its temporal or spatial complexity
Purely periodic beta-expansions in the Pisot non-unit case by V Berthé( Book )

3 editions published in 2002 in English and held by 2 WorldCat member libraries worldwide

 
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Substitutions in dynamics, arithmetics, and combinatorics
Covers
Substitutions in dynamics, arithmetics, and combinatoricsCombinatorics, words and symbolic dynamicsSequences, groups, and number theoryCombinatorics, Words and Symbolic DynamicsCombinatorics
Alternative Names

controlled identityPytheas Fogg, N.

Berthé, V.

Berthé, V. 1957-

Berthé, Valérie

Berthé, Valérie 1957-

Valérie Berthé Frans wiskundige

Valérie Berthé französische Mathematikerin

Valérie Berthé French mathematician

Valérie Berthé matemática francesa

Valérie Berthé matematica francese

Valérie Berthé matematikari frantziarra

ڤاليري بيرتي رياضياتية فرنسية

Languages
English (79)

French (16)