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Author: N. Pytheas Fogg
Publisher: Springer
ISBN: 3540457143
Category : Mathematics
Languages : en
Pages : 411
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Book Description
A certain category of infinite strings of letters on a finite alphabet is presented here, chosen among the 'simplest' possible one may build, both because they are very deterministic and because they are built by simple rules (a letter is replaced by a word, a sequence is produced by iteration). These substitutive sequences have a surprisingly rich structure. The authors describe the concepts of quantity of natural interactions, with combinatorics on words, ergodic theory, linear algebra, spectral theory, geometry of tilings, theoretical computer science, diophantine approximation, trancendence, graph theory. This volume fulfils the need for a reference on the basic definitions and theorems, as well as for a state-of-the-art survey of the more difficult and unsolved problems.
Author: N. Pytheas Fogg
Publisher: Springer
ISBN: 3540457143
Category : Mathematics
Languages : en
Pages : 411
Get Book Here
Book Description
A certain category of infinite strings of letters on a finite alphabet is presented here, chosen among the 'simplest' possible one may build, both because they are very deterministic and because they are built by simple rules (a letter is replaced by a word, a sequence is produced by iteration). These substitutive sequences have a surprisingly rich structure. The authors describe the concepts of quantity of natural interactions, with combinatorics on words, ergodic theory, linear algebra, spectral theory, geometry of tilings, theoretical computer science, diophantine approximation, trancendence, graph theory. This volume fulfils the need for a reference on the basic definitions and theorems, as well as for a state-of-the-art survey of the more difficult and unsolved problems.
Author: Shigeki Akiyama
Publisher: Springer Nature
ISBN: 3030576663
Category : Mathematics
Languages : en
Pages : 468
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Book Description
This book presents a panorama of recent developments in the theory of tilings and related dynamical systems. It contains an expanded version of courses given in 2017 at the research school associated with the Jean-Morlet chair program. Tilings have been designed, used and studied for centuries in various contexts. This field grew significantly after the discovery of aperiodic self-similar tilings in the 60s, linked to the proof of the undecidability of the Domino problem, and was driven futher by Dan Shechtman's discovery of quasicrystals in 1984. Tiling problems establish a bridge between the mutually influential fields of geometry, dynamical systems, aperiodic order, computer science, number theory, algebra and logic. The main properties of tiling dynamical systems are covered, with expositions on recent results in self-similarity (and its generalizations, fusions rules and S-adic systems), algebraic developments connected to physics, games and undecidability questions, and the spectrum of substitution tilings.
Author: Robert Mercaş
Publisher: Springer Nature
ISBN: 3030287963
Category : Mathematics
Languages : en
Pages : 340
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Book Description
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.
Author: Anna Frid
Publisher: Springer Nature
ISBN: 303133180X
Category : Mathematics
Languages : en
Pages : 310
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Book Description
This book constitutes the refereed proceedings of the 14th International Conference on Combinatorics on Words, WORDS 2023, held in Umeå, Sweden, during June 12–16, 2023. The 19 contributed papers presented in this book were carefully reviewed and selected from 28 submissions. In addition, the volume also contains 3 invited papers. WORDS is the main conference series devoted to combinatorics on words. This area is connected to several topics from computer science and mathematics, including string algorithms, automated proofs, discrete dynamics, number theory and, of course, classical combinatorics
Author: Martine Queffélec
Publisher: Springer
ISBN: 3642112129
Category : Mathematics
Languages : en
Pages : 367
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Book Description
This volume mainly deals with the dynamics of finitely valued sequences, and more specifically, of sequences generated by substitutions and automata. Those sequences demonstrate fairly simple combinatorical and arithmetical properties and naturally appear in various domains. As the title suggests, the aim of the initial version of this book was the spectral study of the associated dynamical systems: the first chapters consisted in a detailed introduction to the mathematical notions involved, and the description of the spectral invariants followed in the closing chapters. This approach, combined with new material added to the new edition, results in a nearly self-contained book on the subject. New tools - which have also proven helpful in other contexts - had to be developed for this study. Moreover, its findings can be concretely applied, the method providing an algorithm to exhibit the spectral measures and the spectral multiplicity, as is demonstrated in several examples. Beyond this advanced analysis, many readers will benefit from the introductory chapters on the spectral theory of dynamical systems; others will find complements on the spectral study of bounded sequences; finally, a very basic presentation of substitutions, together with some recent findings and questions, rounds out the book.
Author: Juhani Karhumäki
Publisher: Springer
ISBN: 3642405797
Category : Computers
Languages : en
Pages : 271
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Book Description
This book constitutes the refereed proceedings of the 9th International Conference on Combinatorics on Words, WORDS 2013, held in Turku, Finland, in September 2013 under the auspices of the EATCS. The 20 revised full papers presented were carefully reviewed and selected from 43 initial submissions. The central topic of the conference is combinatorics on words (i.e. the study of finite and infinite sequence of symbols) from varying points of view, including their combinatorial, algebraic and algorithmic aspects, as well as their applications.
Author: Johannes Kellendonk
Publisher: Birkhäuser
ISBN: 3034809034
Category : Mathematics
Languages : en
Pages : 438
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Book Description
What is order that is not based on simple repetition, that is, periodicity? How must atoms be arranged in a material so that it diffracts like a quasicrystal? How can we describe aperiodically ordered systems mathematically? Originally triggered by the – later Nobel prize-winning – discovery of quasicrystals, the investigation of aperiodic order has since become a well-established and rapidly evolving field of mathematical research with close ties to a surprising variety of branches of mathematics and physics. This book offers an overview of the state of the art in the field of aperiodic order, presented in carefully selected authoritative surveys. It is intended for non-experts with a general background in mathematics, theoretical physics or computer science, and offers a highly accessible source of first-hand information for all those interested in this rich and exciting field. Topics covered include the mathematical theory of diffraction, the dynamical systems of tilings or Delone sets, their cohomology and non-commutative geometry, the Pisot substitution conjecture, aperiodic Schrödinger operators, and connections to arithmetic number theory.
Author: Bruce Landman
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110298163
Category : Mathematics
Languages : en
Pages : 1092
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Book Description
"Integers" is a refereed online journal devoted to research in the area of combinatorial number theory. It publishes original research articles in combinatorics and number theory. Topics covered by the journal include additive number theory, multiplicative number theory, sequences and sets, extremal combinatorics, Ramsey theory, elementary number theory, classical combinatorial problems, hypergraphs, and probabilistic number theory. Integers also houses a combinatorial games section. This work presents all papers of the 2013 volume in book form.
Author: Pieter Moree
Publisher: American Mathematical Soc.
ISBN: 147045100X
Category : Education
Languages : en
Pages : 360
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Book Description
This volume contains the proceedings of the conference Dynamics: Topology and Numbers, held from July 2–6, 2018, at the Max Planck Institute for Mathematics, Bonn, Germany. The papers cover diverse fields of mathematics with a unifying theme of relation to dynamical systems. These include arithmetic geometry, flat geometry, complex dynamics, graph theory, relations to number theory, and topological dynamics. The volume is dedicated to the memory of Sergiy Kolyada and also contains some personal accounts of his life and mathematics.
Author: Arnaldo Rodriguez-Gonzalez
Publisher: Arnaldo Rodriguez-Gonzalez
ISBN:
Category : Mathematics
Languages : en
Pages : 493
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Book Description
This largely self-contained textbook on qualitative dynamics and chaos is intended for a broad audience of readers who are interested in describing systems that change over time using a mathematically simple, but conceptually rigorous, framework centered around descriptive sequences of symbols. This framework also allows readers who may not have a large amount of mathematical training to develop an unambiguous understanding of the notion of chaos and related aspects of dynamical systems theory. Concepts and techniques are introduced in the first parts of the book, which are later expanded to more mathematically abstract ideas in the latter parts of the book. For those who are already have some mathematical training, this text is intended to be an alternative to standard symbolic dynamics textbooks which both mildly generalizes their scope and specifically centers its discussion around dynamical systems theory aspects. It uses the notion of a "falsifiable system"—a type of set of infinite symbol sequences, which is an extension of both formal languages and symbolic dynamical systems—as a central conceptual link between the theory of formal languages and the study of chaos, and allows readers a method to identify chaos within such systems (and systems equivalent to them) by entirely graphical methods. The latter parts of the book then focus on how to apply these methods to understand the dynamics of more traditional, numerically-based systems.
