"WORDS", Rouen, 22-27 Septembre 1997 : Special issue of the revue Theoretical Computer Science (J. Néraud Ed.)




Preface by Jean Néraud

The international conference "WORDS" was held in Rouen, France, during the week September 22-26, 1997. About sixty researchers interested in Combinatorics on Words attended this long-awaited event. No simple relation of causality can ever give rise to a system of thinking. Scientific theories are not an exception to the rule of this complex process, where concepts are elaborated, and questions formulated. A systematic study of words first appeared at the beginning of the twenty-iff century, when three now famous papers were published by the Norwegian, Axel Thue (in 1906, 1912, 1914). He explored the properties of infinite words and repetions, and research into these topics is still progressing, as attested by the numerous fruitful studies that were presented at the conference.
Some decades latter in the century, Post would also make use of the concept of Words. Similarly, Words became a basic concept in the combinatorial group theory (the Burnside Problem), in number theory (Van der Waerden's theorem), and in the theory of semigroups, where the concept unifies fundamental results from the theory of Automata, the theory of Complexity, and the study of Formal Languages.
About twenty years ago, Marcel Paul Schützenberger presented a series of questions concerning words. The originality, diversity and difficulty of these questions were the basis of an independent theory of Words. Specific events, such as the meeting "Fête des Mots", organised by Dominique Perrin in 1980, or the first edition of "Combinatorics of Words", published by Lothaire in 1983, have been devoted to the theory. Research will continue in such well-known domains as Codes, Unavoidability, Periodicity, and many others. The present volume collects 14 refered papers, whose results give a good overview of the various topics presented in the conference. These hight quality studies raise numerous questions and open up news areas of research, thus confirming the vitality of the Theory of Words.

Contents



Sturmian Words and related topics

Limit values of the recurrence quotient of Sturmian sequences
Julien Cassaigne

On the combinatorics of finite words
Aldo De Luca

Lyndon Words and Singular Factors of Sturmian words
Guy Melan&cced;on


Repetitions and Periodicity

On abelian squares and substitutions
Arturo Carpi

Fine and Wilf's Theorem for three Periods and a Generalization of Sturmian Words
M. Gabriella Castelli, Filippo Mignosi and Antonio Restivo

The Exact Number of Squares in Fibonacci Words
Aviezri S. Fraenkel, Jamie Simpson


Theory of Codes

On maximal bifix codes
Véronique Bruyère et Dominique Perrin



Equations in the free monoid

Generalized factorizations of words and their algorithmic properties
J. Karhumaki, W. Plandowski, W. Rytter



Extension of the concept of words

Partial words and a theorem of Fine and Wilf
Jean Berstel, Luc Boasson



Words and Enumeration

Transcendence of formal power series with rational coefficients
Jean Paul Allouche

On repetition-free binary words of minimal density
Roman Kolpakov, Gregory Kucherov and Yuri Tarannikov

Complexity for finite factors of infinite sequences
Sébastien Ferenczi and Zoltaán Kása



Algorithmic on words

Constant-Space String-Matching in Sublinear Average Time
Maxime Crochemore, Leszek Gasieniec and Wojciech Rytter

Quasiperiodicity and String Covering
Costas Iliopoulos and Laurent Mouchard
"WORDS"
Special issues
Special issue WORDS, September 99
Special issue WORDS, September 01

atml@free.fr Dernière mise à jour : le 04.03.02