Foundations Of Garside Theory
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Foundations Of Garside Theory
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Author : Patrick Dehornoy
language : en
Publisher: Erich Schmidt Verlag GmbH & Co. KG
Release Date : 2015
Foundations Of Garside Theory written by Patrick Dehornoy and has been published by Erich Schmidt Verlag GmbH & Co. KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Geometric group theory categories.
This text is a monograph on algebra, with connections to geometry and low-dimensional topology. It mainly involves groups, monoids, and categories, and aims to provide a unified treatment for those situations in which one can find distinguished decompositions by iteratively extracting a maximal fragment lying in a prescribed family. Initiated in 1969 by F. A. Garside in the case of Artin's braid groups, this approach led to interesting results in a number of cases, the central notion being what the authors call a Garside family. The study is far from complete, and the purpose of this book is to present the current state of the theory and to invite further research. The book has two parts: In Part A, the bases of a general theory, including many easy examples, are developed. In Part B, various more sophisticated examples are specifically addressed. To make the content accessible to a wide audience of nonspecialists, the book's exposition is essentially self-contained and very few prerequisites are needed. In particular, it should be easy to use this as a textbook both for Garside theory and for the more specialized topics investigated in Part B: Artin-Tits groups, Deligne-Lusztig varieties, groups of algebraic laws, ordered groups, and structure groups of set-theoretic solutions of the Yang-Baxter equation. The first part of the book can be used as the basis for a graduate or advanced undergraduate course.
Fundamentals Of Computation Theory
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Author : Henning Fernau
language : en
Publisher: Springer Nature
Release Date : 2023-09-21
Fundamentals Of Computation Theory written by Henning Fernau and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-21 with Computers categories.
This book constitutes the proceedings of the 24th International Symposium on Fundamentals of Computation Theory, FCT 2023, held in Trier, Germany, in September 2023. The __ full papers included in this volume were carefully reviewed and selected from __ submissions. In addition, the book contains ____ invited talks. The papers cover topics of all aspects of theoretical computer science, in particular algorithms, complexity, formal and logical methods.
Developments In Language Theory
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Author : Igor Potapov
language : en
Publisher: Springer
Release Date : 2015-07-17
Developments In Language Theory written by Igor Potapov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-17 with Computers categories.
This book constitutes the proceedings of the 19th International Conference on Developments in Language Theory, DLT 2015, held in Liverpool, UK. The 31 papers presented together with 5 invited talks were carefully reviewed and selected from 54 submissions. Its scope is very general and includes, among others, 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 bidimensional patterns, cryptography, concurrency, cellular automata, bio-inspired computing, and quantum computing.
Interactions Between Group Theory Symmetry And Cryptology
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Author : María Isabel González Vasco
language : en
Publisher: MDPI
Release Date : 2020-04-22
Interactions Between Group Theory Symmetry And Cryptology written by María Isabel González Vasco and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-22 with Mathematics categories.
Cryptography lies at the heart of most technologies deployed today for secure communications. At the same time, mathematics lies at the heart of cryptography, as cryptographic constructions are based on algebraic scenarios ruled by group or number theoretical laws. Understanding the involved algebraic structures is, thus, essential to design robust cryptographic schemes. This Special Issue is concerned with the interplay between group theory, symmetry and cryptography. The book highlights four exciting areas of research in which these fields intertwine: post-quantum cryptography, coding theory, computational group theory and symmetric cryptography. The articles presented demonstrate the relevance of rigorously analyzing the computational hardness of the mathematical problems used as a base for cryptographic constructions. For instance, decoding problems related to algebraic codes and rewriting problems in non-abelian groups are explored with cryptographic applications in mind. New results on the algebraic properties or symmetric cryptographic tools are also presented, moving ahead in the understanding of their security properties. In addition, post-quantum constructions for digital signatures and key exchange are explored in this Special Issue, exemplifying how (and how not) group theory may be used for developing robust cryptographic tools to withstand quantum attacks.
Geometric And Cohomological Group Theory
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Author : Peter H. Kropholler
language : en
Publisher: Cambridge University Press
Release Date : 2018
Geometric And Cohomological Group Theory written by Peter H. Kropholler 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 2018 with Mathematics categories.
Surveys the state of the art in geometric and cohomological group theory. Ideal entry point for young researchers.
Grobner Shirshov Bases Normal Forms Combinatorial And Decision Problems In Algebra
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Author : Leonid Bokut
language : en
Publisher: World Scientific
Release Date : 2020-06-16
Grobner Shirshov Bases Normal Forms Combinatorial And Decision Problems In Algebra written by Leonid Bokut and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-16 with Mathematics categories.
The book is about (associative, Lie and other) algebras, groups, semigroups presented by generators and defining relations. They play a great role in modern mathematics. It is enough to mention the quantum groups and Hopf algebra theory, the Kac-Moody and Borcherds algebra theory, the braid groups and Hecke algebra theory, the Coxeter groups and semisimple Lie algebra theory, the plactic monoid theory. One of the main problems for such presentations is the problem of normal forms of their elements. Classical examples of such normal forms give the Poincaré-Birkhoff-Witt theorem for universal enveloping algebras and Artin-Markov normal form theorem for braid groups in Burau generators.What is now called Gröbner-Shirshov bases theory is a general approach to the problem. It was created by a Russian mathematician A I Shirshov (1921-1981) for Lie algebras (explicitly) and associative algebras (implicitly) in 1962. A few years later, H Hironaka created a theory of standard bases for topological commutative algebra and B Buchberger initiated this kind of theory for commutative algebras, the Gröbner basis theory. The Shirshov paper was largely unknown outside Russia. The book covers this gap in the modern mathematical literature. Now Gröbner-Shirshov bases method has many applications both for classical algebraic structures (associative, Lie algebra, groups, semigroups) and new structures (dialgebra, pre-Lie algebra, Rota-Baxter algebra, operads). This is a general and powerful method in algebra.
Sequences Groups And Number Theory
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Author : Valérie Berthé
language : en
Publisher: Birkhäuser
Release Date : 2018-04-09
Sequences Groups And Number Theory written by Valérie Berthé and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-09 with Mathematics categories.
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.
Perspectives In Lie Theory
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Author : Filippo Callegaro
language : en
Publisher: Springer
Release Date : 2017-12-07
Perspectives In Lie Theory written by Filippo Callegaro and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-07 with Mathematics categories.
Lie theory is a mathematical framework for encoding the concept of symmetries of a problem, and was the central theme of an INdAM intensive research period at the Centro de Giorgi in Pisa, Italy, in the academic year 2014-2015. This book gathers the key outcomes of this period, addressing topics such as: structure and representation theory of vertex algebras, Lie algebras and superalgebras, as well as hyperplane arrangements with different approaches, ranging from geometry and topology to combinatorics.
Application And Theory Of Petri Nets And Concurrency
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Author : Didier Buchs
language : en
Publisher: Springer Nature
Release Date : 2021-06-16
Application And Theory Of Petri Nets And Concurrency written by Didier Buchs and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-16 with Computers categories.
This book constitutes the proceedings of the 42nd International Conference on Application and Theory of Petri Nets and Concurrency, PETRI NETS 2021, which was held virtually in June 2021. The 22 full papers presented together with 2 keynote papers in this volume were carefully reviewed and selected from 39 submissions. The focus of the conference is on the following topics: application of concurrency to system design; games; verification; synthesis and mining; reachability and partial order; semantics; and tools.
Cataland Why The Fu
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Author : Christian Stump
language : en
Publisher: American Mathematical Soc.
Release Date : 2019
Cataland Why The Fu written by Christian Stump 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 2019 with categories.
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