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Algebraic Combinatorics On Words
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Book Synopsis Algebraic Combinatorics on Words by : M. Lothaire
Download or read book Algebraic Combinatorics on Words written by M. Lothaire and published by Cambridge University Press. This book was released on 2002-04-18 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive 2002 introduction to combinatorics on words for mathematicians and theoretical computer scientists.
Book Synopsis Applied Combinatorics on Words by : M. Lothaire
Download or read book Applied Combinatorics on Words written by M. Lothaire and published by Cambridge University Press. This book was released on 2005-07-11 with total page 646 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher Description
Book Synopsis Combinatorics on Words by : M. Lothaire
Download or read book Combinatorics on Words written by M. Lothaire and published by Cambridge University Press. This book was released on 1997-05-29 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Book Synopsis Patterns in Permutations and Words by : Sergey Kitaev
Download or read book Patterns in Permutations and Words written by Sergey Kitaev and published by Springer Science & Business Media. This book was released on 2011-08-30 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: There has been considerable interest recently in the subject of patterns in permutations and words, a new branch of combinatorics with its roots in the works of Rotem, Rogers, and Knuth in the 1970s. Consideration of the patterns in question has been extremely interesting from the combinatorial point of view, and it has proved to be a useful language in a variety of seemingly unrelated problems, including the theory of Kazhdan—Lusztig polynomials, singularities of Schubert varieties, interval orders, Chebyshev polynomials, models in statistical mechanics, and various sorting algorithms, including sorting stacks and sortable permutations. The author collects the main results in the field in this up-to-date, comprehensive reference volume. He highlights significant achievements in the area, and points to research directions and open problems. The book will be of interest to researchers and graduate students in theoretical computer science and mathematics, in particular those working in algebraic combinatorics and combinatorics on words. It will also be of interest to specialists in other branches of mathematics, theoretical physics, and computational biology. The author collects the main results in the field in this up-to-date, comprehensive reference volume. He highlights significant achievements in the area, and points to research directions and open problems. The book will be of interest to researchers and graduate students in theoretical computer science and mathematics, in particular those working in algebraic combinatorics and combinatorics on words. It will also be of interest to specialists in other branches of mathematics, theoretical physics, and computational biology.
Book Synopsis Bijective Combinatorics by : Nicholas Loehr
Download or read book Bijective Combinatorics written by Nicholas Loehr and published by CRC Press. This book was released on 2011-02-10 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bijective proofs are some of the most elegant and powerful techniques in all of mathematics. Suitable for readers without prior background in algebra or combinatorics, Bijective Combinatorics presents a general introduction to enumerative and algebraic combinatorics that emphasizes bijective methods.The text systematically develops the mathematical
Book Synopsis Combinatorics on Words by : Robert Mercaş
Download or read book Combinatorics on Words written by Robert Mercaş and published by Springer. This book was released on 2019-08-09 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Combinatorics written by Nicholas Loehr and published by CRC Press. This book was released on 2017-08-10 with total page 979 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorics, Second Edition is a well-rounded, general introduction to the subjects of enumerative, bijective, and algebraic combinatorics. The textbook emphasizes bijective proofs, which provide elegant solutions to counting problems by setting up one-to-one correspondences between two sets of combinatorial objects. The author has written the textbook to be accessible to readers without any prior background in abstract algebra or combinatorics. Part I of the second edition develops an array of mathematical tools to solve counting problems: basic counting rules, recursions, inclusion-exclusion techniques, generating functions, bijective proofs, and linear algebraic methods. These tools are used to analyze combinatorial structures such as words, permutations, subsets, functions, graphs, trees, lattice paths, and much more. Part II cover topics in algebraic combinatorics including group actions, permutation statistics, symmetric functions, and tableau combinatorics. This edition provides greater coverage of the use of ordinary and exponential generating functions as a problem-solving tool. Along with two new chapters, several new sections, and improved exposition throughout, the textbook is brimming with many examples and exercises of various levels of difficulty.
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.
Book Synopsis A Course in Combinatorics by : J. H. van Lint
Download or read book A Course in Combinatorics written by J. H. van Lint and published by Cambridge University Press. This book was released on 2001-11-22 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second edition of a popular book on combinatorics, a subject dealing with ways of arranging and distributing objects, and which involves ideas from geometry, algebra and analysis. The breadth of the theory is matched by that of its applications, which include topics as diverse as codes, circuit design and algorithm complexity. It has thus become essential for workers in many scientific fields to have some familiarity with the subject. The authors have tried to be as comprehensive as possible, dealing in a unified manner with, for example, graph theory, extremal problems, designs, colorings and codes. The depth and breadth of the coverage make the book a unique guide to the whole of the subject. The book is ideal for courses on combinatorical mathematics at the advanced undergraduate or beginning graduate level. Working mathematicians and scientists will also find it a valuable introduction and reference.
Book Synopsis Combinatorics of Coxeter Groups by : Anders Bjorner
Download or read book Combinatorics of Coxeter Groups written by Anders Bjorner and published by Springer Science & Business Media. This book was released on 2006-02-25 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: Includes a rich variety of exercises to accompany the exposition of Coxeter groups Coxeter groups have already been exposited from algebraic and geometric perspectives, but this book will be presenting the combinatorial aspects of Coxeter groups
Book Synopsis From Christoffel Words to Markoff Numbers by : Christophe Reutenauer
Download or read book From Christoffel Words to Markoff Numbers written by Christophe Reutenauer and published by Oxford University Press, USA. This book was released on 2019-01-15 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1875, Elwin Bruno Christoffel introduced a special class of words on a binary alphabet linked to continued fractions which would go onto be known as Christoffel words. Some years later, Andrey Markoff published his famous theory, the now called Markoff theory. It characterized certain quadratic forms and certain real numbers by extremal inequalities. Both classes are constructed using certain natural numbers known as Markoff numbers and they are characterized by a certain Diophantine equality. More basically, they are constructed using certain words essentially the Christoffel words. The link between Christoffel words and the theory of Markoff was noted by Ferdinand Frobenius in 1913, but has been neglected in recent times. Motivated by this overlooked connection, this book looks to expand on the relationship between these two areas. Part 1 focuses on the classical theory of Markoff, while Part II explores the more advanced and recent results of the theory of Christoffel words.
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.
Book Synopsis Lessons in Enumerative Combinatorics by : Ömer Eğecioğlu
Download or read book Lessons in Enumerative Combinatorics written by Ömer Eğecioğlu and published by Springer Nature. This book was released on 2021-05-13 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook introduces enumerative combinatorics through the framework of formal languages and bijections. By starting with elementary operations on words and languages, the authors paint an insightful, unified picture for readers entering the field. Numerous concrete examples and illustrative metaphors motivate the theory throughout, while the overall approach illuminates the important connections between discrete mathematics and theoretical computer science. Beginning with the basics of formal languages, the first chapter quickly establishes a common setting for modeling and counting classical combinatorial objects and constructing bijective proofs. From here, topics are modular and offer substantial flexibility when designing a course. Chapters on generating functions and partitions build further fundamental tools for enumeration and include applications such as a combinatorial proof of the Lagrange inversion formula. Connections to linear algebra emerge in chapters studying Cayley trees, determinantal formulas, and the combinatorics that lie behind the classical Cayley–Hamilton theorem. The remaining chapters range across the Inclusion-Exclusion Principle, graph theory and coloring, exponential structures, matching and distinct representatives, with each topic opening many doors to further study. Generous exercise sets complement all chapters, and miscellaneous sections explore additional applications. Lessons in Enumerative Combinatorics captures the authors' distinctive style and flair for introducing newcomers to combinatorics. The conversational yet rigorous presentation suits students in mathematics and computer science at the graduate, or advanced undergraduate level. Knowledge of single-variable calculus and the basics of discrete mathematics is assumed; familiarity with linear algebra will enhance the study of certain chapters.
Book Synopsis Handbook of Enumerative Combinatorics by : Miklos Bona
Download or read book Handbook of Enumerative Combinatorics written by Miklos Bona and published by CRC Press. This book was released on 2015-03-24 with total page 1073 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting the state of the art, the Handbook of Enumerative Combinatorics brings together the work of today's most prominent researchers. The contributors survey the methods of combinatorial enumeration along with the most frequent applications of these methods.This important new work is edited by Miklos Bona of the University of Florida where he
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 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic combinatorics is the study of combinatorial objects as an extension of the study of finite permutation groups, or, in other words, group theory without groups. In the spirit of Delsarte's theory, this book studies combinatorial objects such as graphs, codes, designs, etc. in the general framework of association schemes, providing a comprehensive overview of the theory as well as pointing out to extensions.
