Download or read book Topics on Combinatorial Semigroups written by Yuqi Guo and published by Springer Nature. This book was released on with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Semigroups and Combinatorial Applications written by Gerard Lallement and published by John Wiley & Sons. This book was released on 1979 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to present those parts of the theory of semigroups that are directly related to automata theory, algebraic linguistics, and combinatorics. Publications in these mathematical disciplines contained methods and results pertaining to the algebraic theory of semigroups, and this has contributed to considerable enrichment of the theory, enlargement of its scope, and improved its potential to become a major domain of algebra. Semigroup theory appears to provide a general framework for unifying and clarifying a number of topics in fields that at first sight appear unrelated. This book is intended as a textbook for graduate students in mathematics and computer science, and as a reference book for researchers interested in associative structures.
Download or read book Topics in Combinatorial Semigroup Theory written by Victor Maltcev and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Semigroups written by K. P. Shum and published by . This book was released on 1998 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first International Conference on Semigroups and its Related Topics, held in Kunming, China, 1995, celebrated the establishment of the Institute of Pure Mathematics at Yunnan University, Kunming. The event attracted mathematicians from around the world, who contributed talks and papers on the new developments of semigroups and its applications. These included topics on algebraic semigroups, combinatorial semigroups, computer languages, codings, and universal algebras. Since the conference, the papers have been re-edited, and in some cases revised, and are now cummulated into this review volume, making it a lasting reference book on the development of Semigroup theory. Some survey articles written by experts in the field, and which were not presented at the conference, are also included in this book.
Download or read book Topics in Combinatorial Semigroup Theory written by Victor Maltcev and published by . This book was released on 2012 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis we discuss various topics from Combinatorial Semigroup Theory: automaton semigroups; finiteness conditions and their preservation under certain semigroup theoretic notions of index; Markov semigroups; word-hyperbolic semigroups; decision problems for finitely presented and one-relator monoids. First, in order to show that general ideas from Combinatorial Semigroup Theory can apply to uncountable semigroups, at the beginning of the thesis we discuss semigroups with Bergman's property. We prove that an automaton semigroup generated by a Cayley machine of a finite semigroup S is itself finite if and only if S is aperiodic, which yields a new characterisation of finite aperiodic monoids. Using this, we derive some further results about Cayley automaton semigroups. We investigate how various semigroup finiteness conditions, linked to the notion of ideal, are preserved under finite Rees and Green indices. We obtain a surprising result that J = D is preserved by supersemigroups of finite Green index, but it is not preserved by subsemigroups of finite Rees index even in the finitely generated case. We also consider the question of preservation of hopficity for finite Rees index. We prove that in general hopficity is preserved neither by finite Rees index subsemigroups, nor by finite Rees index extensions. However, under finite generation assumption, hopficity is preserved by finite Rees index extensions. Still, there is an example of a finitely generated hopfian semigroup with a non-hopfian subsemigroup of finite Rees index. We prove also that monoids presented by confluent context-free monadic rewriting systems are word-hyperbolic, and provide an example of such a monoid, which does not admit a word-hyperbolic structure with uniqueness. This answers in the negative a question of Duncan & Gilman. We initiate in this thesis a study of Markov semigroups. We investigate how the property of being Markov is preserved under finite Rees and Green indices. For various semigroup properties P we examine whether P , ¬P are Markov properties, and whether P is decidable for finitely presented and one-relator monoids.
Download or read book Combinatorics on Words written by Larry J. Cummings and published by Academic Press. This book was released on 2014-05-10 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorics on Words: Progress and Perspectives covers the proceedings of an international meeting by the same title, held at the University of Waterloo, Canada on August 16-22, 1982. This meeting highlights the diverse aspects of combinatorics on words, including the Thue systems, topological dynamics, combinatorial group theory, combinatorics, number theory, and computer science. This book is organized into four parts encompassing 19 chapters. The first part describes the Thue systems with the Church-Rosser property. A Thue system will be called "Church-Rosser if two strings are congruent with respect to that system if and only if they have a common descendant, that is, a string that can be obtained applying only rewriting rules that reduce length. The next part deals with the problems related to the encoding of codes and the overlapping of words in rational languages. This part also explores the features of polynomially bounded DOL systems yield codes. These topics are followed by discussions of some combinatorial properties of metrics over the free monoid and the burnside problem of semigroups of matrices. The last part considers the ambiguity types of formal grammars, finite languages, computational complexity of algebraic structures, and the Bracket-context tree functions. This book will be of value to mathematicians and advance undergraduate and graduate students.
Download or read book Topics in Combinatorial Group Theory written by Gilbert Baumslag and published by Birkhäuser. This book was released on 2012-12-06 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial group theory is a loosely defined subject, with close connections to topology and logic. With surprising frequency, problems in a wide variety of disciplines, including differential equations, automorphic functions and geometry, have been distilled into explicit questions about groups, typically of the following kind: Are the groups in a given class finite (e.g., the Burnside problem)? Finitely generated? Finitely presented? What are the conjugates of a given element in a given group? What are the subgroups of that group? Is there an algorithm for deciding for every pair of groups in a given class whether they are isomorphic or not? The objective of combinatorial group theory is the systematic development of algebraic techniques to settle such questions. In view of the scope of the subject and the extraordinary variety of groups involved, it is not surprising that no really general theory exists. These notes, bridging the very beginning of the theory to new results and developments, are devoted to a number of topics in combinatorial group theory and serve as an introduction to the subject on the graduate level.
Download or read book Words Languages and Combinatorics Three written by Masami It? and published by World Scientific. This book was released on 2003 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: The research results published in this book range from pure mathematical theory (semigroup theory, discrete mathematics, etc.) to theoretical computer science, in particular formal languages and automata. The papers address issues in the algebraic and combinatorial theories of semigroups, words and languages, the structure theory of automata, the classification theory of formal languages and codes, and applications of these theories to various areas, like quantum and molecular computing, coding theory, and cryptography.
Download or read book Combinatorial Algebra Syntax and Semantics written by Mark V. Sapir and published by Springer. This book was released on 2014-10-06 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial Algebra: Syntax and Semantics provides comprehensive account of many areas of combinatorial algebra. It contains self-contained proofs of more than 20 fundamental results, both classical and modern. This includes Golod–Shafarevich and Olshanskii's solutions of Burnside problems, Shirshov's solution of Kurosh's problem for PI rings, Belov's solution of Specht's problem for varieties of rings, Grigorchuk's solution of Milnor's problem, Bass–Guivarc'h theorem about growth of nilpotent groups, Kleiman's solution of Hanna Neumann's problem for varieties of groups, Adian's solution of von Neumann-Day's problem, Trahtman's solution of the road coloring problem of Adler, Goodwyn and Weiss. The book emphasize several ``universal" tools, such as trees, subshifts, uniformly recurrent words, diagrams and automata. With over 350 exercises at various levels of difficulty and with hints for the more difficult problems, this book can be used as a textbook, and aims to reach a wide and diversified audience. No prerequisites beyond standard courses in linear and abstract algebra are required. The broad appeal of this textbook extends to a variety of student levels: from advanced high-schoolers to undergraduates and graduate students, including those in search of a Ph.D. thesis who will benefit from the “Further reading and open problems” sections at the end of Chapters 2 –5. The book can also be used for self-study, engaging those beyond t he classroom setting: researchers, instructors, students, virtually anyone who wishes to learn and better understand this important area of mathematics.
Download or read book The Analytical and Topological Theory of Semigroups written by Karl Heinrich Hofmann and published by de Gruyter. This book was released on 1990 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents trends and developments in diverse areas of semigroup theory such as analysis, functional analysis and topology. Main topics include: Lie theory and algebraic geometry for semigroups; structure theory of compact semigroups; functional analysis on semigroups; relations to systems theory and a combinatorial number theory. Particular emphasis is given to applications in probability theory and semigroups of continuous functions. Annotation copyrighted by Book News, Inc., Portland, OR
Download or read book Classical Finite Transformation Semigroups written by Olexandr Ganyushkin and published by Springer Science & Business Media. This book was released on 2008-12-10 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this monograph is to give a self-contained introduction to the modern theory of finite transformation semigroups with a strong emphasis on concrete examples and combinatorial applications. It covers the following topics on the examples of the three classical finite transformation semigroups: transformations and semigroups, ideals and Green's relations, subsemigroups, congruences, endomorphisms, nilpotent subsemigroups, presentations, actions on sets, linear representations, cross-sections and variants. The book contains many exercises and historical comments and is directed first of all to both graduate and postgraduate students looking for an introduction to the theory of transformation semigroups, but also to tutors and researchers.
Download or read book Combinatorial Number Theory and Additive Group Theory written by Alfred Geroldinger and published by Springer Science & Business Media. This book was released on 2009-06-04 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Combinatorial Group Theory written by Roger C. Lyndon and published by Springer. This book was released on 2015-03-12 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "This book [...] defines the boundaries of the subject now called combinatorial group theory. [...] it is a considerable achievement to have concentrated a survey of the subject into 339 pages. [...] a valuable and welcome addition to the literature, containing many results not previously available in a book. It will undoubtedly become a standard reference." Mathematical Reviews
Download or read book Words Languages And Combinatorics Ii Proceedings Of The International Conference written by Masami Ito and published by World Scientific. This book was released on 1994-09-19 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: The research results published in this set of proceedings range from pure semigroup theory to theoretical computer science, in particular formal languages and automata. Contributed by internationally recognized researchers, the papers address issues in the algebraic and combinatorial theories of semigroups, the structure theory of automata, the classification theory of formal languages and codes and applications of these theories to various areas like circuit testing, coding theory, or cryptography. The underlying theme is the semigroup and automaton theories and their role in certain applications.
Download or read book The Unity of Combinatorics written by Richard K. Guy and published by American Mathematical Soc.. This book was released on 2020-05-12 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorics, or the art and science of counting, is a vibrant and active area of pure mathematical research with many applications. The Unity of Combinatorics succeeds in showing that the many facets of combinatorics are not merely isolated instances of clever tricks but that they have numerous connections and threads weaving them together to form a beautifully patterned tapestry of ideas. Topics include combinatorial designs, combinatorial games, matroids, difference sets, Fibonacci numbers, finite geometries, Pascal's triangle, Penrose tilings, error-correcting codes, and many others. Anyone with an interest in mathematics, professional or recreational, will be sure to find this book both enlightening and enjoyable. Few mathematicians have been as active in this area as Richard Guy, now in his eighth decade of mathematical productivity. Guy is the author of over 300 papers and twelve books in geometry, number theory, graph theory, and combinatorics. In addition to being a life-long number-theorist and combinatorialist, Guy's co-author, Ezra Brown, is a multi-award-winning expository writer. Together, Guy and Brown have produced a book that, in the spirit of the founding words of the Carus book series, is accessible “not only to mathematicians but to scientific workers and others with a modest mathematical background.”
Download or read book Finiteness and Regularity in Semigroups and Formal Languages written by Aldo de Luca and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a rigorous and self-contained monograph on a central topic in theoretical computer science. For the first time in book form, original results from the last ten years are presented, some previously unpublished, using combinatorial and algebraic methods. These are mainly based on combinatorics on words and especially on the theory of "unavoidable regularities." Researchers will find important new results on semigroups and formal languages, as well as various applications for these methods.
Download or read book Algebraic Combinatorics on Words written by M. Lothaire and published by . This book was released on 2002 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorics on words has arisen independently within several branches of mathematics, for instance number theory, group theory and probability, and appears frequently in problems related to theoretical computer science. The first unified treatment of the area was given in Lothaire's book Combinatorics on Words. Originally published in 2002, this book presents several more topics and provides deeper insights into subjects discussed in the previous volume. An introductory chapter provides the reader with all the necessary background material. There are numerous examples, full proofs whenever possible and a notes section discussing further developments in the area. This book is both a comprehensive introduction to the subject and a valuable reference source for researchers.
