## New Publications O ered by the AMS

L.

L. Scott, Some new highest weight categories; I. Pop and

A.

Stolin, Classification of quasi-trigonometric solutions of the

classical Yang-Baxter equation; C. M. Ringel, The relevance and the ubiquity of Prüfer modules; A. Savage, Quivers and the Euclidean group; S. Shang and Y. Gao, u_{2}-Lie admissible algebras and Steinberg unitary Lie algebras; T. Shoji, Lusztig’s conjecture for finite classical groups with even characteristic; Y. Su, A survey on quasifinite representations of Weyl type Lie algebras; N. Xi, Maximal and primitive elements in baby Verma modules for type B_{2}; Y.-F. Yao and B. Shu, Irreducible representations of the special algebras in prime characteristic.

Contemporary Mathematics, Volume 478

February 2009, 295 pages, Softcover, ISBN: 978-0-8218-4555-4, LC 2008034291, 2000 Mathematics Subject Classification: 16Gxx, 17Bxx, 20Cxx, 20Gxx; 17B10, 17B20, 17B37, 17B45, 17B56, 20G05, 20G10, 20G42, 20C05, 20C08, 20C30, AMS members US$71, List US$89, Order code CONM/478

# Applications

Combinatorics on Words

Christo el Words and Repetitions in Words

Jean Berstel, Université de Marne-la-Vallée, France, Aaron Lauve, Texas A&M University, College Station, TX, and Christophe Reutenauer and Franco V. Saliola, Université du Québec à Montréal, QC, Canada

The two parts of this text are based on two series of lectures delivered by Jean Berstel and Christophe Reutenauer in March 2007 at the Centre de Recherches Mathématiques, Montréal, Canada. Part I represents the first modern and comprehensive exposition of the theory of Christo el words. Part II presents numerous combinatorial and algorithmic aspects of repetition-free words stemming from the work of Axel Thue—a pioneer in the theory of combinatorics on words.

A beginner to the theory of combinatorics on words will be motivated by the numerous examples, and the large variety of exercises, which make the book unique at this level of exposition. The clean and streamlined exposition and the extensive bibliography will also be appreciated. After reading this book, beginners should be ready to read modern research papers in this rapidly growing field and contribute their own research to its development.

Experienced readers will be interested in the finitary approach to Sturmian words that Christo el words o er, as well as the novel geometric and algebraic approach chosen for their exposition. They will also appreciate the historical presentation of the Thue–Morse word and its applications and the novel results on Abelian repetition-free words.

This item will also be of interest to those working in analysis and number theory.

Titles in this series are co-published with the Centre de Recherches Mathématiques.

### Contents: Part

I.

### Christo

el

words: Christo

el words; Christo

el

morphisms; Standard factorization; Palindromization; Primitive elements in the free group F_{2}; Characterizations; Continued fractions; The theory of Marko numbers; Part II. Repetitions in words: The Thue–Morse word; Combinatorics of the Thue–Morse

word; Square-free words; Squares patterns; Bibliography; Index.

in

words;

Repetitions

and

CRM Monograph Series, Volume 27

January 2009, 147 pages, Hardcover, ISBN: 978-0-8218-4480-9, LC 2008036669, 2000 Mathematics Subject Classification: 68R15; 37B10, 11J70, 68W40, AMS members US$41, List US$51, Order code CRMM/27

# Recent Trends in Cryptography

Ignacio Luengo, Universidad Complutense de Madrid, Spain, Editor

This volume contains articles representing the courses given at the 2005 RSME Santaló Summer School on “Recent Trends in Cryptography”. The main goal of the Summer School was to present some of the recent mathematical methods used in cryptography and cryptanalysis. The School was oriented to graduate and doctoral students, as well as recent doctorates. The material is presented in an expository manner with many examples and references.

The topics in this volume cover some of the most interesting new developments in public key and symmetric key cryptography, such as pairing based cryptography and lattice based cryptanalysis.

This item will also be of interest to those working in number theory.

This book is copublished by the Real Sociedad Matemática Española and the American Mathematical Society.

Contents: A. Fúster-Sabater, Cellular automata in stream ciphers; T. Helleseth, Linear and nonlinear sequences and applications to stream ciphers; A. Menezes, An introduction to pairing-based cryptography; P. Q. Nguyen, Public-key cryptanalysis; I. E. Shparlinski, Pseudorandom number generators from elliptic curves.

Contemporary Mathematics, Volume 477

February 2009, 141 pages, Softcover, ISBN: 978-0-8218-3984-3, LC 2008033089, 2000 Mathematics Subject Classification: 94Axx, 94A60, 94A62, 11T71, 14G50, 68P25, 14H52, AMS members US$39, List US$49, Order code CONM/477

76

Notices of the AMS

Volume 56 Number 1