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From Christoffel Words To Markoff Numbers
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Book Synopsis From Christoffel Words to Markoff Numbers by : Christophe Reutenauer
Download or read book From Christoffel Words to Markoff Numbers written by Christophe Reutenauer and published by Oxford University Press, USA. This book was released on 2019-01-15 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Combinatorics on Words written by and published by American Mathematical Soc.. This book was released on with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Computation and Combinatorics in Dynamics, Stochastics and Control by : Elena Celledoni
Download or read book Computation and Combinatorics in Dynamics, Stochastics and Control written by Elena Celledoni and published by Springer. This book was released on 2019-01-13 with total page 734 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Abel Symposia volume at hand contains a collection of high-quality articles written by the world’s leading experts, and addressing all mathematicians interested in advances in deterministic and stochastic dynamical systems, numerical analysis, and control theory. In recent years we have witnessed a remarkable convergence between individual mathematical disciplines that approach deterministic and stochastic dynamical systems from mathematical analysis, computational mathematics and control theoretical perspectives. Breakthrough developments in these fields now provide a common mathematical framework for attacking many different problems related to differential geometry, analysis and algorithms for stochastic and deterministic dynamics. In the Abel Symposium 2016, which took place from August 16-19 in Rosendal near Bergen, leading researchers in the fields of deterministic and stochastic differential equations, control theory, numerical analysis, algebra and random processes presented and discussed the current state of the art in these diverse fields. The current Abel Symposia volume may serve as a point of departure for exploring these related but diverse fields of research, as well as an indicator of important current and future developments in modern mathematics.
Book Synopsis Markov's Theorem and 100 Years of the Uniqueness Conjecture by : Martin Aigner
Download or read book Markov's Theorem and 100 Years of the Uniqueness Conjecture written by Martin Aigner and published by Springer Science & Business Media. This book was released on 2013-07-18 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book takes the reader on a mathematical journey, from a number-theoretic point of view, to the realm of Markov’s theorem and the uniqueness conjecture, gradually unfolding many beautiful connections until everything falls into place in the proof of Markov’s theorem. What makes the Markov theme so attractive is that it appears in an astounding variety of different fields, from number theory to combinatorics, from classical groups and geometry to the world of graphs and words. On the way, there are also introductory forays into some fascinating topics that do not belong to the standard curriculum, such as Farey fractions, modular and free groups, hyperbolic planes, and algebraic words. The book closes with a discussion of the current state of knowledge about the uniqueness conjecture, which remains an open challenge to this day. All the material should be accessible to upper-level undergraduates with some background in number theory, and anything beyond this level is fully explained in the text. This is not a monograph in the usual sense concentrating on a specific topic. Instead, it narrates in five parts – Numbers, Trees, Groups, Words, Finale – the story of a discovery in one field and its many manifestations in others, as a tribute to a great mathematical achievement and as an intellectual pleasure, contemplating the marvellous unity of all mathematics.
Book Synopsis Combinatorics on Words by : Thierry Lecroq
Download or read book Combinatorics on Words written by Thierry Lecroq and published by Springer Nature. This book was released on 2021-09-06 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 13th International Conference on Combinatorics on Words, WORDS 2021, held virtually in September 2021. The 14 revised full papers presented in this book together with 2 invited talks were carefully reviewed and selected from 18 submissions. WORDS is the main conference series devoted to the mathematical theory of words. In particular, the combinatorial, algebraic and algorithmic aspects of words are emphasized. Motivations may also come from other domains such as theoretical computer science, bioinformatics, digital geometry, symbolic dynamics, numeration systems, text processing, number theory, etc.
Book Synopsis Combinatorics on Words by : Robert Mercaş
Download or read book Combinatorics on Words written by Robert Mercaş and published by Springer Nature. This book was released on 2019-09-02 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 12th International Conference on Combinatorics on Words, WORDS 2019, held in Loughborough, UK, in September 2019. The 21 revised full papers presented in this book together with 5 invited talks were carefully reviewed and selected from 34 submissions. WORDS is the main conference series devoted to the mathematical theory of words. In particular, the combinatorial, algebraic and algorithmic aspects of words are emphasized. Motivations may also come from other domains such as theoretical computer science, bioinformatics, digital geometry, symbolic dynamics, numeration systems, text processing, number theory, etc.
Book Synopsis Dimension Groups and Dynamical Systems by : Fabien Durand
Download or read book Dimension Groups and Dynamical Systems written by Fabien Durand and published by Cambridge University Press. This book was released on 2022-01-31 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first self-contained exposition of the fascinating link between dynamical systems and dimension groups. The authors explore the rich interplay between topological properties of dynamical systems and the algebraic structures associated with them, with an emphasis on symbolic systems, particularly substitution systems. It is recommended for anybody with an interest in topological and symbolic dynamics, automata theory or combinatorics on words. Intended to serve as an introduction for graduate students and other newcomers to the field as well as a reference for established researchers, the book includes a thorough account of the background notions as well as detailed exposition – with full proofs – of the major results of the subject. A wealth of examples and exercises, with solutions, serve to build intuition, while the many open problems collected at the end provide jumping-off points for future research.
Book Synopsis Combinatorics on Words by : Jean Berstel
Download or read book Combinatorics on Words written by Jean Berstel and published by American Mathematical Soc.. This book was released on 2009 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Algebraic Informatics by : Symeon Bozapalidis
Download or read book Algebraic Informatics written by Symeon Bozapalidis and published by Springer Science & Business Media. This book was released on 2007-12-14 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Second International Conference on Algebraic Informatics, CAI 2007, held in Thessaloniki, Greece, in May 2007. The 10 revised full papers presented together with 9 invited papers were carefully reviewed and selected from 29 submissions. The papers cover topics such as algebraic semantics on graphs and trees, formal power series, syntactic objects, algebraic picture processing, infinite computation, acceptors and transducers for strings, trees, graphs, arrays, etc., and decision problems.
Book Synopsis Combinatorics on Words by : Srečko Brlek
Download or read book Combinatorics on Words written by Srečko Brlek and published by Springer. This book was released on 2017-08-21 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Combinatorics on Words written by and published by . This book was released on 2009 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 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, whi.
Book Synopsis Mathematical Foundations of Computer Science 1996 by : Wojciech Penczek
Download or read book Mathematical Foundations of Computer Science 1996 written by Wojciech Penczek and published by Springer Science & Business Media. This book was released on 1996-08-07 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 21st International Symposium on Mathematical Foundations of Computer Science, MFCS '96, held in Crakow, Poland in September 1996. The volume presents 35 revised full papers selected from a total of 95 submissions together with 8 invited papers and 2 abstracts of invited talks. The papers included cover issues from the whole area of theoretical computer science, with a certain emphasis on mathematical and logical foundations. The 10 invited presentations are of particular value.
Book Synopsis Gesammelte Abhandlungen by : Ferdinand Georg Frobenius
Download or read book Gesammelte Abhandlungen written by Ferdinand Georg Frobenius and published by . This book was released on 1968 with total page 748 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Orthogonal Polynomials by : Gábor Szegő
Download or read book Orthogonal Polynomials written by Gábor Szegő and published by . This book was released on 1967 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Mathematical Intelligencer written by and published by . This book was released on 1985 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Christofell, E. B. by : Elwin Bruno Christoffel
Download or read book Christofell, E. B. written by Elwin Bruno Christoffel and published by Birkhäuser. This book was released on 1981 with total page 798 pages. Available in PDF, EPUB and Kindle. Book excerpt: This memorial volume is dedicated to E. B. Christoffel on the occasion of the 150th anniversary of his birth. Its aim is, on the one hand, to present the life of Christoffel and the scientific milieu in which he worked and, on the other hand, to present a survey of his work not only in its historical context but especially in the frame of contemporary mathematics and physics. For one thing, this book contains expanded versions of the twelve invited lectures given at the International Christoffel Symposium, held on November 8- 11, 1979 at Aachen and Monschau. For another, the scope of these papers has been broadened by soliciting some fourty-five additional invited articles, concerned either with further aspects of the work of Christoffel or with specia lized topics in fields in which Christoffel had worked. This should give the reader a greater opportunity to appreciate the richness of Christoffel's contributions to the mathematical and physical sciences, and not only its immediate impact but also its subsequent infiuence. It can be discerned that Christoffel did basic work not only in differential geometry or, better still, in classical tensor analysis, thereby supplying the mathematical foundations of Einstein's theory of general relativity, but also in a variety of other areas of mathematics. The scope of Christoffel's work can be appreciated from the following synopsis of the thirteen chapters into which the festschrift is divided. Chap."
Download or read book Location of Zeros written by George Pólya and published by . This book was released on 1974 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
