Christophe Reutenauer – författare
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13 produkter
13 produkter
E-bok
PDF, Engelska, 20181 282 kr
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In 1875, Elwin Bruno Christoffel introduced a special class of words on a binary alphabet linked to continued fractions which would go onto be known as Christoffel words. Some years later, Andrey Markoff published his famous theory, the now called Markoff theory. It characterized certain quadratic forms and certain real numbers by extremal inequalities. Both classes are constructed using certain natural numbers — known as Markoff numbers — and they arecharacterized by a certain Diophantine equality. More basically, they are constructed using certain words — essentially the Christoffel words.The link between Christoffel words and the theory of Markoff was noted by Ferdinand Frobenius in 1913, but has been neglected in recent times. Motivated by this overlooked connection, this book looks to expand on the relationship between these two areas. Part 1 focuses on the classical theory of Markoff, while Part II explores the more advanced and recent results of the theory of Christoffel words.
- Nyhet
Inbunden, Engelska, 2026
1 530 kr
Skickas inom 5-8 vardagar
In 1875, Elwin Bruno Christoffel introduced a special class of words on a binary alphabet linked to continued fractions which would go on to be known as Christoffel words. Some years later, Andrey Markoff published his famous theory, now called the Markoff theory. Markoff's theory characterized certain quadratic forms and real numbers by extremal inequalities. Both classes are constructed using certain natural numbers, known as Markoff numbers, and they form part of a solution to the Markoff Diophantine equation. More basically, they are constructed using certain words, essentially Christoffel words.The link between Christoffel words and Markoff's theory was noted by Ferdinand Frobenius in 1913, but has been neglected in recent times. Motivated by this overlooked connection, this book looks to expand on the relationship between these two areas. The first part of the book focuses on the classical theory of Markoff, while Part II explores the more advanced and recent results of the theory of Christoffel words. This new edition includes many additional exercises and solutions, as well as expanded sections on quadratic forms and quadratic numbers, two new chapters on standard words and the commutator subgroup, and revised results in combinatorics on words.
Del 7 - London Mathematical Society Monographs
Free Lie Algebras
Inbunden, Engelska, 1993
4 041 kr
Skickas inom 7-10 vardagar
Although Lie polynomials first appeared at the turn of the century, there have been many recent developments especially from the point of view of representation theory. This book covers all aspects, with emphasis on the algebraic and combinatorial point of view as well as representation theory.
Inbunden, Engelska, 2018
1 243 kr
Skickas inom 5-8 vardagar
In 1875, Elwin Bruno Christoffel introduced a special class of words on a binary alphabet linked to continued fractions which would go onto be known as Christoffel words. Some years later, Andrey Markoff published his famous theory, the now called Markoff theory. It characterized certain quadratic forms and certain real numbers by extremal inequalities. Both classes are constructed using certain natural numbers — known as Markoff numbers — and they are characterized by a certain Diophantine equality. More basically, they are constructed using certain words — essentially the Christoffel words. The link between Christoffel words and the theory of Markoff was noted by Ferdinand Frobenius in 1913, but has been neglected in recent times. Motivated by this overlooked connection, this book looks to expand on the relationship between these two areas. Part 1 focuses on the classical theory of Markoff, while Part II explores the more advanced and recent results of the theory of Christoffel words.
Del 137 - Encyclopedia of Mathematics and its Applications
Noncommutative Rational Series with Applications
Inbunden, Engelska, 2010
1 634 kr
Skickas inom 7-10 vardagar
The algebraic theory of automata was created by Schützenberger and Chomsky over 50 years ago and there has since been a great deal of development. Classical work on the theory to noncommutative power series has been augmented more recently to areas such as representation theory, combinatorial mathematics and theoretical computer science. This book presents to an audience of graduate students and researchers a modern account of the subject and its applications. The algebraic approach allows the theory to be developed in a general form of wide applicability. For example, number-theoretic results can now be more fully explored, in addition to applications in automata theory, codes and non-commutative algebra. Much material, for example, Schützenberger's theorem on polynomially bounded rational series, appears here for the first time in book form. This is an excellent resource and reference for all those working in algebra, theoretical computer science and their areas of overlap.
Inbunden, Engelska, 2009
1 461 kr
Skickas inom 11-20 vardagar
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 Mathematiques, Montreal, Canada. Part I represents the first modern and comprehensive exposition of the theory of Christoffel 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 Christoffel words offer, 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.
Del 10432 - Lecture Notes in Computer Science
Combinatorics on Words
11th International Conference, WORDS 2017, Montréal, QC, Canada, September 11-15, 2017, Proceedings
Häftad, Engelska, 2017
544 kr
Skickas inom 10-15 vardagar
This book constitutes the refereed proceedings of the 11th International Conference on Combinatorics on Words, WORDS 2017, held in Montréal, QC, Canada, in September 2017. The 21 revised full papers presented together with 5invoted talks were carefully reviewed and selected from 26 submissions. Discrete geometry plays an expanding role in the fields of shape modeling, image synthesis, and image analysis. It deals with topological and geometrical definitions of digitized objects or digitized images and provides both a theoretical and computational framework for computer imaging.
E-bok
Engelska, 2017712 kr
Läs direkt efter köp
This book constitutes the refereed proceedings of the 11th International Conference on Combinatorics on Words, WORDS 2017, held in Montréal, QC, Canada, in September 2017.
The 21 revised full papers presented together with 5invoted talks were carefully reviewed and selected from 26 submissions. Discrete geometry plays an expanding role in the fields of shape modeling, image synthesis, and image analysis. It deals with topological and geometrical definitions of digitized objects or digitized images and provides both a theoretical and computational framework for computer imaging.
Häftad, Engelska, 2009
1 113 kr
Skickas inom 10-15 vardagar
This book constitutes the refereed proceedings of the 15th IAPR International Conference on Discrete Geometry for Computer Imagery, DGCI 2009, held in Montréal, Canada, in September/October 2009. The 42 revised full papers were carefully reviewed and selected from numerous submissions. The papers are organized in topical sections on discrete shape, representation, recognition and analysis; discrete and combinatorial tools for image segmentation and analysis; discrete and combinatorial Topology; models for discrete geometry; geometric transforms; and discrete tomography.
E-bok
PDF, Engelska, 20091 416 kr
Läs direkt efter köp
This book constitutes the refereed proceedings of the 15th IAPR International Conference on Discrete Geometry for Computer Imagery, DGCI 2009, held in Montréal, Canada, in September/October 2009. The 42 revised full papers were carefully reviewed and selected from numerous submissions. The papers are organized in topical sections on discrete shape, representation, recognition and analysis; discrete and combinatorial tools for image segmentation and analysis; discrete and combinatorial Topology; models for discrete geometry; geometric transforms; and discrete tomography.
Häftad, Engelska, 2016
544 kr
Skickas inom 10-15 vardagar
This book constitutes the proceedings of the 20th International Conference on Developments in Language Theory, DLT 2016, held in Montreal, QC, Canada, in July 2016.The 32 full papers and 4 abstracts of invited papers presented were carefully reviewed and selected from 48 submissions. This volume presents current developments in formal languages and automata, especially from the following topics and areas: combinatorial and algebraic properties of words and languages; grammars, acceptors and transducers for strings, trees, graphs, arrays; algebraic theories for automata and languages; codes; efficient text algorithms; symbolic dynamics; decision problems; relationships to complexity theory and logic; picture description and analysis; polyominoes and bidimentional patterns; cryptography; concurrency; cellular automata; bio-inspried computing; quantum computing.
E-bok
PDF, Engelska, 2016712 kr
Läs direkt efter köp
This book constitutes the proceedings of the 20th International Conference on Developments in Language Theory, DLT 2016, held in Montreal, QC, Canada, in July 2016.
The 32 full papers and 4 abstracts of invited papers presented were carefully reviewed and selected from 48 submissions. This volume presents current developments in formal languages and automata, especially from the following topics and areas: combinatorial and algebraic properties of words and languages; grammars, acceptors and transducers for strings, trees, graphs, arrays; algebraic theories for automata and languages; codes; efficient text algorithms; symbolic dynamics; decision problems; relationships to complexity theory and logic; picture description and analysis; polyominoes and bidimentional patterns; cryptography; concurrency; cellular automata; bio-inspried computing; quantum computing.
Del 129 - Encyclopedia of Mathematics and its Applications
Codes and Automata
Inbunden, Engelska, 2009
2 334 kr
Tillfälligt slut
This major revision of Berstel and Perrin's classic Theory of Codes has been rewritten with a more modern focus and a much broader coverage of the subject. The concept of unambiguous automata, which is intimately linked with that of codes, now plays a significant role throughout the book, reflecting developments of the last 20 years. This is complemented by a discussion of the connection between codes and automata, and new material from the field of symbolic dynamics. The authors have also explored links with more practical applications, including data compression and cryptography. The treatment remains self-contained: there is background material on discrete mathematics, algebra and theoretical computer science. The wealth of exercises and examples make it ideal for self-study or courses. In sum this is a comprehensive reference on the theory of variable-length codes and their relation to automata.