Combinatorial Algebra Syntax And Semantics

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Combinatorial Algebra: Syntax and Semantics

Author : Mark V. Sapir
Publisher : Springer
ISBN 13 : 3319080318
Total Pages : 369 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Combinatorial Algebra: Syntax and Semantics by : Mark V. Sapir

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.

Algorithmic and Combinatorial Algebra

Author : L.A. Bokut'
Publisher : Springer Science & Business Media
ISBN 13 : 9401120021
Total Pages : 399 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Algorithmic and Combinatorial Algebra by : L.A. Bokut'

Download or read book Algorithmic and Combinatorial Algebra written by L.A. Bokut' and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: Even three decades ago, the words 'combinatorial algebra' contrasting, for in stance, the words 'combinatorial topology,' were not a common designation for some branch of mathematics. The collocation 'combinatorial group theory' seems to ap pear first as the title of the book by A. Karras, W. Magnus, and D. Solitar [182] and, later on, it served as the title of the book by R. C. Lyndon and P. Schupp [247]. Nowadays, specialists do not question the existence of 'combinatorial algebra' as a special algebraic activity. The activity is distinguished not only by its objects of research (that are effectively given to some extent) but also by its methods (ef fective to some extent). To be more exact, we could approximately define the term 'combinatorial algebra' for the purposes of this book, as follows: So we call a part of algebra dealing with groups, semi groups , associative algebras, Lie algebras, and other algebraic systems which are given by generators and defining relations {in the first and particular place, free groups, semigroups, algebras, etc. )j a part in which we study universal constructions, viz. free products, lINN-extensions, etc. j and, finally, a part where specific methods such as the Composition Method (in other words, the Diamond Lemma, see [49]) are applied. Surely, the above explanation is far from covering the full scope of the term (compare the prefaces to the books mentioned above).

Grobner-shirshov Bases: Normal Forms, Combinatorial And Decision Problems In Algebra

Author : Leonid Bokut
Publisher : World Scientific
ISBN 13 : 9814619507
Total Pages : 308 pages
Book Rating : 4.8/5 (146 download)

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Book Synopsis Grobner-shirshov Bases: Normal Forms, Combinatorial And Decision Problems In Algebra by : Leonid Bokut

Download or read book Grobner-shirshov Bases: Normal Forms, Combinatorial And Decision Problems In Algebra written by Leonid Bokut and published by World Scientific. This book was released on 2020-06-16 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Combinatorics on Words

Author : Larry J. Cummings
Publisher : Academic Press
ISBN 13 : 1483264688
Total Pages : 416 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Combinatorics on Words by : Larry J. Cummings

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.

Combinatorial Commutative Algebra

Author : Ezra Miller
Publisher : Springer Science & Business Media
ISBN 13 : 9780387237077
Total Pages : 442 pages
Book Rating : 4.2/5 (37 download)

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Book Synopsis Combinatorial Commutative Algebra by : Ezra Miller

Download or read book Combinatorial Commutative Algebra written by Ezra Miller and published by Springer Science & Business Media. This book was released on 2005-06-21 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent developments are covered Contains over 100 figures and 250 exercises Includes complete proofs

Investigations in Algebraic Theory of Combinatorial Objects

Author : I.A. Faradzev
Publisher : Springer Science & Business Media
ISBN 13 : 9780792319276
Total Pages : 534 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Investigations in Algebraic Theory of Combinatorial Objects by : I.A. Faradzev

Download or read book Investigations in Algebraic Theory of Combinatorial Objects written by I.A. Faradzev and published by Springer Science & Business Media. This book was released on 1993-11-30 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: X Köchendorffer, L.A. Kalu:lnin and their students in the 50s and 60s. Nowadays the most deeply developed is the theory of binary invariant relations and their combinatorial approximations. These combinatorial approximations arose repeatedly during this century under various names (Hecke algebras, centralizer rings, association schemes, coherent configurations, cellular rings, etc.-see the first paper of the collection for details) andin various branches of mathematics, both pure and applied. One of these approximations, the theory of cellular rings (cellular algebras), was developed at the end of the 60s by B. Yu. Weisfeiler and A.A. Leman in the course of the first serious attempt to study the complexity of the graph isomorphism problem, one of the central problems in the modern theory of combinatorial algorithms. At roughly the same time G.M. Adelson-Velskir, V.L. Arlazarov, I.A. Faradtev and their colleagues had developed a rather efficient tool for the constructive enumeration of combinatorial objects based on the branch and bound method. By means of this tool a number of "sports-like" results were obtained. Some of these results are still unsurpassed.

Advances in Algebra and Combinatorics

Author : K. P. Shum
Publisher : World Scientific
ISBN 13 : 9812790004
Total Pages : 384 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Advances in Algebra and Combinatorics by : K. P. Shum

Download or read book Advances in Algebra and Combinatorics written by K. P. Shum and published by World Scientific. This book was released on 2008 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a compilation of lectures on algebras and combinatorics presented at the Second International Congress in Algebra and Combinatorics. It reports on not only new results, but also on open problems in the field. The proceedings volume is useful for graduate students and researchers in algebras and combinatorics. Contributors include eminent figures such as V Artamanov, L Bokut, J Fountain, P Hilton, M Jambu, P Kolesnikov, Li Wei and K Ueno.

The Generation Problem in Thompson Group $F$

Author : Gili Golan Polak
Publisher : American Mathematical Society
ISBN 13 : 1470467232
Total Pages : 106 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis The Generation Problem in Thompson Group $F$ by : Gili Golan Polak

Download or read book The Generation Problem in Thompson Group $F$ written by Gili Golan Polak and published by American Mathematical Society. This book was released on 2024-01-26 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Advances In Algebra And Combinatorics - Proceedings Of The Second International Congress In Algebra And Combinatorics

Author : Kar Ping Shum
Publisher : World Scientific
ISBN 13 : 9814472131
Total Pages : 384 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Advances In Algebra And Combinatorics - Proceedings Of The Second International Congress In Algebra And Combinatorics by : Kar Ping Shum

Download or read book Advances In Algebra And Combinatorics - Proceedings Of The Second International Congress In Algebra And Combinatorics written by Kar Ping Shum and published by World Scientific. This book was released on 2008-06-17 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a compilation of lectures on algebras and combinatorics presented at the Second International Congress in Algebra and Combinatorics. It reports on not only new results, but also on open problems in the field. The proceedings volume is useful for graduate students and researchers in algebras and combinatorics. Contributors include eminent figures such as V Artamanov, L Bokut, J Fountain, P Hilton, M Jambu, P Kolesnikov, Li Wei and K Ueno.

Combinatorial Theory

Author : Martin Aigner
Publisher : Springer Science & Business Media
ISBN 13 : 3642591019
Total Pages : 493 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Combinatorial Theory by : Martin Aigner

Download or read book Combinatorial Theory written by Martin Aigner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a well-organized, easy-to-follow introduction to combinatorial theory, with examples, notes and exercises. ". . . a very good introduction to combinatorics. This book can warmly be recommended first of all to students interested in combinatorics." Publicationes Mathematicae Debrecen

Algebraic Combinatorics

Author : Eiichi Bannai
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110627736
Total Pages : 303 pages
Book Rating : 4.1/5 (16 download)

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Book Synopsis Algebraic Combinatorics by : Eiichi Bannai

Download or read book Algebraic Combinatorics written by Eiichi Bannai and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-02-22 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This series is devoted to the publication of high-level monographs which cover the whole spectrum of current discrete mathematics and its applications in various fields. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of discrete mathematics. Contributions which are on the borderline of discrete mathematics and related fields and which stimulate further research at the crossroads of these areas are particularly welcome.

Hyperidentities: Boolean And De Morgan Structures

Author : Yuri Movsisyan
Publisher : World Scientific
ISBN 13 : 9811254931
Total Pages : 561 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Hyperidentities: Boolean And De Morgan Structures by : Yuri Movsisyan

Download or read book Hyperidentities: Boolean And De Morgan Structures written by Yuri Movsisyan and published by World Scientific. This book was released on 2022-09-20 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hyperidentities are important formulae of second-order logic, and research in hyperidentities paves way for the study of second-order logic and second-order model theory.This book illustrates many important current trends and perspectives for the field of hyperidentities and their applications, of interest to researchers in modern algebra and discrete mathematics. It covers a number of directions, including the characterizations of the Boolean algebra of n-ary Boolean functions and the distributive lattice of n-ary monotone Boolean functions; the classification of hyperidentities of the variety of lattices, the variety of distributive (modular) lattices, the variety of Boolean algebras, and the variety of De Morgan algebras; the characterization of algebras with aforementioned hyperidentities; the functional representations of finitely-generated free algebras of various varieties of lattices and bilattices via generalized Boolean functions (De Morgan functions, quasi-De Morgan functions, super-Boolean functions, super-De Morgan functions, etc); the structural results for De Morgan algebras, Boole-De Morgan algebras, super-Boolean algebras, bilattices, among others.While problems of Boolean functions theory are well known, the present book offers alternative, more general problems, involving the concepts of De Morgan functions, quasi-De Morgan functions, super-Boolean functions, and super-De Morgan functions, etc. In contrast to other generalized Boolean functions discovered and investigated so far, these functions have clearly normal forms. This quality is of crucial importance for their applications in pure and applied mathematics, especially in discrete mathematics, quantum computation, quantum information theory, quantum logic, and the theory of quantum computers.

Language and Automata Theory and Applications

Author : Carlos Martín-Vide
Publisher : Springer
ISBN 13 : 3030134350
Total Pages : 470 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Language and Automata Theory and Applications by : Carlos Martín-Vide

Download or read book Language and Automata Theory and Applications written by Carlos Martín-Vide and published by Springer. This book was released on 2019-03-12 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 13th International Conference on Language and Automata Theory and Applications, LATA 2019, held in St. Petersburg, Russia, in March 2019. The 31 revised full papers presented together with 5 invited talks were carefully reviewed and selected from 98 submissions. The papers cover the following topics: Automata; Complexity; Grammars; Languages; Graphs, trees and rewriting; and Words and codes.

Advances in the Theory of Varieties of Semigroups

Author : Edmond W. H. Lee
Publisher : Springer Nature
ISBN 13 : 3031164970
Total Pages : 286 pages
Book Rating : 4.0/5 (311 download)

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Book Synopsis Advances in the Theory of Varieties of Semigroups by : Edmond W. H. Lee

Download or read book Advances in the Theory of Varieties of Semigroups written by Edmond W. H. Lee and published by Springer Nature. This book was released on 2023-05-10 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph thoroughly explores the development of the theory of varieties of semigroups and of two related algebras: involution semigroups and monoids. Through this in-depth analysis, readers will attain a deeper understanding of the differences between these three types of varieties, which may otherwise seem counterintuitive. New results with detailed proofs are also presented that answer previously unsolved fundamental problems. Featuring both a comprehensive overview as well as highlighting the author’s own significant contributions to the area, this book will help establish this subfield as a matter of timely interest. Advances in the Theory of Varieties of Semigroups will appeal to researchers in universal algebra and will be particularly valuable for specialists in semigroups.

Fields of Logic and Computation II

Author : Lev D. Beklemishev
Publisher : Springer
ISBN 13 : 3319235346
Total Pages : 330 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Fields of Logic and Computation II by : Lev D. Beklemishev

Download or read book Fields of Logic and Computation II written by Lev D. Beklemishev and published by Springer. This book was released on 2015-09-05 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Festschrift is published in honor of Yuri Gurevich's 75th birthday. Yuri Gurevich has made fundamental contributions on the broad spectrum of logic and computer science, including decision procedures, the monadic theory of order, abstract state machines, formal methods, foundations of computer science, security, and much more. Many of these areas are reflected in the 20 articles in this Festschrift and in the presentations at the "Yurifest" symposium, which was held in Berlin, Germany, on September 11 and 12, 2015. The Yurifest symposium was co-located with the 24th EACSL Annual Conference on Computer Science Logic (CSL 2015).

Combinatory Linguistics

Author : Cem Bozsahin
Publisher : Walter de Gruyter
ISBN 13 : 311029687X
Total Pages : 304 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Combinatory Linguistics by : Cem Bozsahin

Download or read book Combinatory Linguistics written by Cem Bozsahin and published by Walter de Gruyter. This book was released on 2012-12-06 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book examines to what extent the mediating relation between constituents and their semantics can arise from combinatory knowledge of words. It traces the roots of Combinatory Categorial Grammar, and uses the theory to promote a Humean question in linguistics and cognitive science: Why do we see limited constituency and dependency in natural languages, despite their diversity and potential infinity? A potential answer is that constituents and dependencies might have arisen from a single resource: adjacency. The combinatory formulation of adjacency constrains possible grammars.

Computations and Combinatorics in Commutative Algebra

Author : Anna M. Bigatti
Publisher : Springer
ISBN 13 : 3319513192
Total Pages : 136 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Computations and Combinatorics in Commutative Algebra by : Anna M. Bigatti

Download or read book Computations and Combinatorics in Commutative Algebra written by Anna M. Bigatti and published by Springer. This book was released on 2017-03-14 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: Featuring up-to-date coverage of three topics lying at the intersection of combinatorics and commutative algebra, namely Koszul algebras, primary decompositions and subdivision operations in simplicial complexes, this book has its focus on computations. "Computations and Combinatorics in Commutative Algebra" has been written by experts in both theoretical and computational aspects of these three subjects and is aimed at a broad audience, from experienced researchers who want to have an easy but deep review of the topics covered to postgraduate students who need a quick introduction to the techniques. The computational treatment of the material, including plenty of examples and code, will be useful for a wide range of professionals interested in the connections between commutative algebra and combinatorics.