Combinatorics Automata And Number Theory

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Combinatorics, Automata and Number Theory

Valérie Berthé,Michel Rigo
Combinatorics Automata and Number Theory Book PDF

Author : Valérie Berthé,Michel Rigo
Publisher : Cambridge University Press
Page : 637 pages
File Size : 40,8 Mb
Release : 2010-08-12
Category : Mathematics
ISBN : 9781139643184

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Combinatorics, Automata and Number Theory by Valérie Berthé,Michel Rigo Pdf

This collaborative volume presents trends arising from the fruitful interaction between the themes of combinatorics on words, automata and formal language theory, and number theory. Presenting several important tools and concepts, the authors also reveal some of the exciting and important relationships that exist between these different fields. Topics include numeration systems, word complexity function, morphic words, Rauzy tilings and substitutive dynamical systems, Bratelli diagrams, frequencies and ergodicity, Diophantine approximation and transcendence, asymptotic properties of digital functions, decidability issues for D0L systems, matrix products and joint spectral radius. Topics are presented in a way that links them to the three main themes, but also extends them to dynamical systems and ergodic theory, fractals, tilings and spectral properties of matrices. Graduate students, research mathematicians and computer scientists working in combinatorics, theory of computation, number theory, symbolic dynamics, fractals, tilings and stringology will find much of interest in this book.

Combinatorics, Automata and Number Theory

Valérie Berthé,Michel Rigo
Combinatorics Automata and Number Theory Book PDF

Author : Valérie Berthé,Michel Rigo
Publisher : Cambridge University Press
Page : 637 pages
File Size : 51,5 Mb
Release : 2010-08-12
Category : Mathematics
ISBN : 9780521515979

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Combinatorics, Automata and Number Theory by Valérie Berthé,Michel Rigo Pdf

This series is devoted to significant topics or themes that have wide application in mathematics or mathematical science and for which a detailed development of the abstract theory is less important than a thorough and concrete exploration of the implications and applications. Books in the Encyclopedia of Mathematics and its Applications cover their subjects comprehensively. Less important results may be summarised as exercises at the ends of chapters, For technicalities, readers can be referred to the bibliography, which is expected to be comprehensive. As a result, volumes are encyclopedic references or manageable guides to major subjects.

Sequences, Groups, and Number Theory

Valérie Berthé,Michel Rigo
Sequences Groups and Number Theory Book PDF

Author : Valérie Berthé,Michel Rigo
Publisher : Birkhäuser
Page : 578 pages
File Size : 49,8 Mb
Release : 2018-04-09
Category : Mathematics
ISBN : 9783319691527

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Sequences, Groups, and Number Theory by Valérie Berthé,Michel Rigo Pdf

This collaborative book presents recent trends on the study of sequences, including combinatorics on words and symbolic dynamics, and new interdisciplinary links to group theory and number theory. Other chapters branch out from those areas into subfields of theoretical computer science, such as complexity theory and theory of automata. The book is built around four general themes: number theory and sequences, word combinatorics, normal numbers, and group theory. Those topics are rounded out by investigations into automatic and regular sequences, tilings and theory of computation, discrete dynamical systems, ergodic theory, numeration systems, automaton semigroups, and amenable groups. This volume is intended for use by graduate students or research mathematicians, as well as computer scientists who are working in automata theory and formal language theory. With its organization around unified themes, it would also be appropriate as a supplemental text for graduate level courses.

Combinatorics, Automata, and Number Theory

Michel Rigo
Combinatorics Automata and Number Theory Book PDF

Author : Michel Rigo
Publisher : Unknown
Page : 636 pages
File Size : 42,6 Mb
Release : 2010
Category : Combinatorial analysis
ISBN : 1139635271

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Combinatorics, Automata, and Number Theory by Michel Rigo Pdf

This collaborative volume presents recent trends arising from the fruitful interaction between combinatorics on words, automata and number theory.

Formal Languages, Automata and Numeration Systems 1

Michel Rigo
Formal Languages Automata and Numeration Systems 1 Book PDF

Author : Michel Rigo
Publisher : John Wiley & Sons
Page : 330 pages
File Size : 49,8 Mb
Release : 2014-11-17
Category : Computers
ISBN : 9781848216150

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Formal Languages, Automata and Numeration Systems 1 by Michel Rigo Pdf

Formal Languages, Automaton and Numeration Systems presents readers with a review of research related to formal language theory, combinatorics on words or numeration systems, such as Words, DLT (Developments in Language Theory), ICALP, MFCS (Mathematical Foundation of Computer Science), Mons Theoretical Computer Science Days, Numeration, CANT (Combinatorics, Automata and Number Theory). Combinatorics on words deals with problems that can be stated in a non-commutative monoid, such as subword complexity of finite or infinite words, construction and properties of infinite words, unavoidable regularities or patterns. When considering some numeration systems, any integer can be represented as a finite word over an alphabet of digits. This simple observation leads to the study of the relationship between the arithmetical properties of the integers and the syntactical properties of the corresponding representations. One of the most profound results in this direction is given by the celebrated theorem by Cobham. Surprisingly, a recent extension of this result to complex numbers led to the famous Four Exponentials Conjecture. This is just one example of the fruitful relationship between formal language theory (including the theory of automata) and number theory.

Combinatorics and Number Theory of Counting Sequences

Istvan Mezo
Combinatorics and Number Theory of Counting Sequences Book PDF

Author : Istvan Mezo
Publisher : CRC Press
Page : 480 pages
File Size : 48,6 Mb
Release : 2019-08-19
Category : Computers
ISBN : 9781351346382

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Combinatorics and Number Theory of Counting Sequences by Istvan Mezo Pdf

Combinatorics and Number Theory of Counting Sequences is an introduction to the theory of finite set partitions and to the enumeration of cycle decompositions of permutations. The presentation prioritizes elementary enumerative proofs. Therefore, parts of the book are designed so that even those high school students and teachers who are interested in combinatorics can have the benefit of them. Still, the book collects vast, up-to-date information for many counting sequences (especially, related to set partitions and permutations), so it is a must-have piece for those mathematicians who do research on enumerative combinatorics. In addition, the book contains number theoretical results on counting sequences of set partitions and permutations, so number theorists who would like to see nice applications of their area of interest in combinatorics will enjoy the book, too. Features The Outlook sections at the end of each chapter guide the reader towards topics not covered in the book, and many of the Outlook items point towards new research problems. An extensive bibliography and tables at the end make the book usable as a standard reference. Citations to results which were scattered in the literature now become easy, because huge parts of the book (especially in parts II and III) appear in book form for the first time.

Automatic Sequences

Jean-Paul Allouche,Jeffrey Shallit
Automatic Sequences Book PDF

Author : Jean-Paul Allouche,Jeffrey Shallit
Publisher : Cambridge University Press
Page : 592 pages
File Size : 45,6 Mb
Release : 2003-07-21
Category : Computers
ISBN : 0521823323

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Automatic Sequences by Jean-Paul Allouche,Jeffrey Shallit Pdf

Uniting dozens of seemingly disparate results from different fields, this book combines concepts from mathematics and computer science to present the first integrated treatment of sequences generated by 'finite automata'. The authors apply the theory to the study of automatic sequences and their generalizations, such as Sturmian words and k-regular sequences. And further, they provide applications to number theory (particularly to formal power series and transcendence in finite characteristic), physics, computer graphics, and music. Starting from first principles wherever feasible, basic results from combinatorics on words, numeration systems, and models of computation are discussed. Thus this book is suitable for graduate students or advanced undergraduates, as well as for mature researchers wishing to know more about this fascinating subject. Results are presented from first principles wherever feasible, and the book is supplemented by a collection of 460 exercises, 85 open problems, and over 1600 citations to the literature.

Combinatorial Number Theory and Additive Group Theory

Alfred Geroldinger,Imre Ruzsa
Combinatorial Number Theory and Additive Group Theory Book PDF

Author : Alfred Geroldinger,Imre Ruzsa
Publisher : Springer Science & Business Media
Page : 324 pages
File Size : 48,6 Mb
Release : 2009-04-15
Category : Mathematics
ISBN : 9783764389611

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Combinatorial Number Theory and Additive Group Theory by Alfred Geroldinger,Imre Ruzsa Pdf

Additive combinatorics is a relatively recent term coined to comprehend the developments of the more classical additive number theory, mainly focussed on problems related to the addition of integers. Some classical problems like the Waring problem on the sum of k-th powers or the Goldbach conjecture are genuine examples of the original questions addressed in the area. One of the features of contemporary additive combinatorics is the interplay of a great variety of mathematical techniques, including combinatorics, harmonic analysis, convex geometry, graph theory, probability theory, algebraic geometry or ergodic theory. This book gathers the contributions of many of the leading researchers in the area and is divided into three parts. The two first parts correspond to the material of the main courses delivered, Additive combinatorics and non-unique factorizations, by Alfred Geroldinger, and Sumsets and structure, by Imre Z. Ruzsa. The third part collects the notes of most of the seminars which accompanied the main courses, and which cover a reasonably large part of the methods, techniques and problems of contemporary additive combinatorics.

Fundamental Number Theory with Applications

Richard A. Mollin
Fundamental Number Theory with Applications Book PDF

Author : Richard A. Mollin
Publisher : CRC Press
Page : 382 pages
File Size : 54,8 Mb
Release : 2008-02-21
Category : Mathematics
ISBN : 9781420066616

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Fundamental Number Theory with Applications by Richard A. Mollin Pdf

An update of the most accessible introductory number theory text available, Fundamental Number Theory with Applications, Second Edition presents a mathematically rigorous yet easy-to-follow treatment of the fundamentals and applications of the subject. The substantial amount of reorganizing makes this edition clearer and more elementary in its coverage. New to the Second Edition • Removal of all advanced material to be even more accessible in scope • New fundamental material, including partition theory, generating functions, and combinatorial number theory • Expanded coverage of random number generation, Diophantine analysis, and additive number theory • More applications to cryptography, primality testing, and factoring • An appendix on the recently discovered unconditional deterministic polynomial-time algorithm for primality testing Taking a truly elementary approach to number theory, this text supplies the essential material for a first course on the subject. Placed in highlighted boxes to reduce distraction from the main text, nearly 70 biographies focus on major contributors to the field. The presentation of over 1,300 entries in the index maximizes cross-referencing so students can find data with ease.

Introduction to Number Theory

Anthony Vazzana,Martin Erickson,David Garth
Introduction to Number Theory Book PDF

Author : Anthony Vazzana,Martin Erickson,David Garth
Publisher : CRC Press
Page : 537 pages
File Size : 52,6 Mb
Release : 2007-10-30
Category : Mathematics
ISBN : 9781584889373

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Introduction to Number Theory by Anthony Vazzana,Martin Erickson,David Garth Pdf

One of the oldest branches of mathematics, number theory is a vast field devoted to studying the properties of whole numbers. Offering a flexible format for a one- or two-semester course, Introduction to Number Theory uses worked examples, numerous exercises, and two popular software packages to describe a diverse array of number theory topics. This classroom-tested, student-friendly text covers a wide range of subjects, from the ancient Euclidean algorithm for finding the greatest common divisor of two integers to recent developments that include cryptography, the theory of elliptic curves, and the negative solution of Hilbert’s tenth problem. The authors illustrate the connections between number theory and other areas of mathematics, including algebra, analysis, and combinatorics. They also describe applications of number theory to real-world problems, such as congruences in the ISBN system, modular arithmetic and Euler’s theorem in RSA encryption, and quadratic residues in the construction of tournaments. The book interweaves the theoretical development of the material with Mathematica® and MapleTM calculations while giving brief tutorials on the software in the appendices. Highlighting both fundamental and advanced topics, this introduction provides all of the tools to achieve a solid foundation in number theory.

The Logical Approach to Automatic Sequences

Jeffrey Shallit
The Logical Approach to Automatic Sequences Book PDF

Author : Jeffrey Shallit
Publisher : Cambridge University Press
Page : 376 pages
File Size : 53,6 Mb
Release : 2022-09-30
Category : Computers
ISBN : 9781108786973

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The Logical Approach to Automatic Sequences by Jeffrey Shallit Pdf

Automatic sequences are sequences over a finite alphabet generated by a finite-state machine. This book presents a novel viewpoint on automatic sequences, and more generally on combinatorics on words, by introducing a decision method through which many new results in combinatorics and number theory can be automatically proved or disproved with little or no human intervention. This approach to proving theorems is extremely powerful, allowing long and error-prone case-based arguments to be replaced by simple computations. Readers will learn how to phrase their desired results in first-order logic, using free software to automate the computation process. Results that normally require multipage proofs can emerge in milliseconds, allowing users to engage with mathematical questions that would otherwise be difficult to solve. With more than 150 exercises included, this text is an ideal resource for researchers, graduate students, and advanced undergraduates studying combinatorics, sequences, and number theory.

Combinatorial and Additive Number Theory IV

Melvyn B. Nathanson
Combinatorial and Additive Number Theory IV Book PDF

Author : Melvyn B. Nathanson
Publisher : Springer Nature
Page : 445 pages
File Size : 49,7 Mb
Release : 2021-08-12
Category : Mathematics
ISBN : 9783030679965

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Combinatorial and Additive Number Theory IV by Melvyn B. Nathanson Pdf

This is the fourth in a series of proceedings of the Combinatorial and Additive Number Theory (CANT) conferences, based on talks from the 2019 and 2020 workshops at the City University of New York. The latter was held online due to the COVID-19 pandemic, and featured speakers from North and South America, Europe, and Asia. The 2020 Zoom conference was the largest CANT conference in terms of the number of both lectures and participants. These proceedings contain 25 peer-reviewed and edited papers on current topics in number theory. Held every year since 2003 at the CUNY Graduate Center, the workshop surveys state-of-the-art open problems in combinatorial and additive number theory and related parts of mathematics. Topics featured in this volume include sumsets, zero-sum sequences, minimal complements, analytic and prime number theory, Hausdorff dimension, combinatorial and discrete geometry, and Ramsey theory. This selection of articles will be of relevance to both researchers and graduate students interested in current progress in number theory.

Formal Languages, Automata and Numeration Systems 2

Michel Rigo
Formal Languages Automata and Numeration Systems 2 Book PDF

Author : Michel Rigo
Publisher : John Wiley & Sons
Page : 151 pages
File Size : 48,7 Mb
Release : 2014-09-10
Category : Technology & Engineering
ISBN : 9781119042860

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Formal Languages, Automata and Numeration Systems 2 by Michel Rigo Pdf

The interplay between words, computability, algebra and arithmetic has now proved its relevance and fruitfulness. Indeed, the cross-fertilization between formal logic and finite automata (such as that initiated by J.R. Büchi) or between combinatorics on words and number theory has paved the way to recent dramatic developments, for example, the transcendence results for the real numbers having a "simple" binary expansion, by B. Adamczewski and Y. Bugeaud. This book is at the heart of this interplay through a unified exposition. Objects are considered with a perspective that comes both from theoretical computer science and mathematics. Theoretical computer science offers here topics such as decision problems and recognizability issues, whereas mathematics offers concepts such as discrete dynamical systems. The main goal is to give a quick access, for students and researchers in mathematics or computer science, to actual research topics at the intersection between automata and formal language theory, number theory and combinatorics on words. The second of two volumes on this subject, this book covers regular languages, numeration systems, formal methods applied to decidability issues about infinite words and sets of numbers.

Combinatorics on Words

M. Lothaire
Combinatorics on Words Book PDF

Author : M. Lothaire
Publisher : Cambridge University Press
Page : 260 pages
File Size : 43,6 Mb
Release : 1997-05-29
Category : Mathematics
ISBN : 9780521599245

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Combinatorics on Words by M. Lothaire Pdf

Combinatorics on words, or finite sequences, is a field which grew simultaneously within disparate branches of mathematics such as group theory and probability. It has grown into an independent theory finding substantial applications in computer science automata theory and liguistics. This volume is the first to present a thorough treatment of this theory. All of the main results and techniques are covered. The presentation is accessible to undergraduate and graduate level students in mathematics and computer science as well as to specialists in all branches of applied mathematics.

Combinatorial and Additive Number Theory

Melvyn B. Nathanson
Combinatorial and Additive Number Theory Book PDF

Author : Melvyn B. Nathanson
Publisher : Springer
Page : 309 pages
File Size : 53,7 Mb
Release : 2014-10-18
Category : Mathematics
ISBN : 9781493916016

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Combinatorial and Additive Number Theory by Melvyn B. Nathanson Pdf

This proceedings volume is based on papers presented at the Workshops on Combinatorial and Additive Number Theory (CANT), which were held at the Graduate Center of the City University of New York in 2011 and 2012. The goal of the workshops is to survey recent progress in combinatorial number theory and related parts of mathematics. The workshop attracts researchers and students who discuss the state-of-the-art, open problems and future challenges in number theory.