From Christoffel Words To Markoff Numbers
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From Christoffel Words To Markoff Numbers
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Author : Christophe Reutenauer
language : en
Publisher:
Release Date : 2019
From Christoffel Words To Markoff Numbers written by Christophe Reutenauer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Mathematics categories.
This book looks to expand on the relationship between Christoffel words and Markoff theory. Part 1 focuses on the classical theory of Markoff, while part II explores the more advanced and recent results around Christoffel words.
Combinatorics On Words
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Author :
language : en
Publisher: American Mathematical Soc.
Release Date :
Combinatorics On Words written by and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
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.
Open Problems In Algebraic Combinatorics
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Author : Christine Berkesch
language : en
Publisher: American Mathematical Society
Release Date : 2024-08-21
Open Problems In Algebraic Combinatorics written by Christine Berkesch and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-21 with Mathematics categories.
In their preface, the editors describe algebraic combinatorics as the area of combinatorics concerned with exact, as opposed to approximate, results and which puts emphasis on interaction with other areas of mathematics, such as algebra, topology, geometry, and physics. It is a vibrant area, which saw several major developments in recent years. The goal of the 2022 conference Open Problems in Algebraic Combinatorics 2022 was to provide a forum for exchanging promising new directions and ideas. The current volume includes contributions coming from the talks at the conference, as well as a few other contributions written specifically for this volume. The articles cover the majority of topics in algebraic combinatorics with the aim of presenting recent important research results and also important open problems and conjectures encountered in this research. The editors hope that this book will facilitate the exchange of ideas in algebraic combinatorics.
Computation And Combinatorics In Dynamics Stochastics And Control
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Author : Elena Celledoni
language : en
Publisher: Springer
Release Date : 2019-01-13
Computation And Combinatorics In Dynamics Stochastics And Control written by Elena Celledoni and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-13 with Mathematics categories.
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.
Combinatorics On Words
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Author : Thierry Lecroq
language : en
Publisher: Springer Nature
Release Date : 2021-09-06
Combinatorics On Words written by Thierry Lecroq and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-06 with Mathematics categories.
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.
Markov S Theorem And 100 Years Of The Uniqueness Conjecture
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Author : Martin Aigner
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-07-18
Markov S Theorem And 100 Years Of The Uniqueness Conjecture written by Martin Aigner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-18 with Mathematics categories.
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.
Combinatorics On Words
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Author : Robert Mercaş
language : en
Publisher: Springer Nature
Release Date : 2019-09-02
Combinatorics On Words written by Robert Mercaş and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-02 with Mathematics categories.
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.
Dimension Groups And Dynamical Systems
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Author : Fabien Durand
language : en
Publisher: Cambridge University Press
Release Date : 2022-02-03
Dimension Groups And Dynamical Systems written by Fabien Durand and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-03 with Mathematics categories.
This is the first self-contained exposition of the connections between symbolic dynamical systems, dimension groups and Bratteli diagrams.
Introduction To Differential Geometry
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Author : Joel W. Robbin
language : en
Publisher: Springer Nature
Release Date : 2022-01-12
Introduction To Differential Geometry written by Joel W. Robbin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-12 with Mathematics categories.
This textbook is suitable for a one semester lecture course on differential geometry for students of mathematics or STEM disciplines with a working knowledge of analysis, linear algebra, complex analysis, and point set topology. The book treats the subject both from an extrinsic and an intrinsic view point. The first chapters give a historical overview of the field and contain an introduction to basic concepts such as manifolds and smooth maps, vector fields and flows, and Lie groups, leading up to the theorem of Frobenius. Subsequent chapters deal with the Levi-Civita connection, geodesics, the Riemann curvature tensor, a proof of the Cartan-Ambrose-Hicks theorem, as well as applications to flat spaces, symmetric spaces, and constant curvature manifolds. Also included are sections about manifolds with nonpositive sectional curvature, the Ricci tensor, the scalar curvature, and the Weyl tensor. An additional chapter goes beyond the scope of a one semester lecture course and deals with subjects such as conjugate points and the Morse index, the injectivity radius, the group of isometries and the Myers-Steenrod theorem, and Donaldson's differential geometric approach to Lie algebra theory.
Algebraic Informatics
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Author : Symeon Bozapalidis
language : en
Publisher: Springer
Release Date : 2007-12-06
Algebraic Informatics written by Symeon Bozapalidis and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-06 with Computers categories.
This book constitutes the refereed proceedings of the Second International Conference on Algebraic Informatics, CAI 2007, held in Thessaloniki, Greece, in May 2007. 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.