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| Author | : M. Lothaire |
| Publisher | : Cambridge University Press |
| Total Pages | : 536 |
| Release | : 2002-04-18 |
| Genre | : Mathematics |
| ISBN | : 9780521812207 |
Comprehensive 2002 introduction to combinatorics on words for mathematicians and theoretical computer scientists.
| Author | : M. Lothaire |
| Publisher | : Cambridge University Press |
| Total Pages | : 646 |
| Release | : 2005-07-11 |
| Genre | : Computers |
| ISBN | : 9780521848022 |
Publisher Description
| Author | : M. Lothaire |
| Publisher | : Cambridge University Press |
| Total Pages | : 260 |
| Release | : 1997-05-29 |
| Genre | : Mathematics |
| ISBN | : 0521599245 |
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.
| Author | : Eiichi Bannai |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 303 |
| Release | : 2021-02-22 |
| Genre | : Mathematics |
| ISBN | : 3110627736 |
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.
| Author | : Richard P. Stanley |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 226 |
| Release | : 2013-06-17 |
| Genre | : Mathematics |
| ISBN | : 1461469988 |
Written by one of the foremost experts in the field, Algebraic Combinatorics is a unique undergraduate textbook that will prepare the next generation of pure and applied mathematicians. The combination of the author’s extensive knowledge of combinatorics and classical and practical tools from algebra will inspire motivated students to delve deeply into the fascinating interplay between algebra and combinatorics. Readers will be able to apply their newfound knowledge to mathematical, engineering, and business models. The text is primarily intended for use in a one-semester advanced undergraduate course in algebraic combinatorics, enumerative combinatorics, or graph theory. Prerequisites include a basic knowledge of linear algebra over a field, existence of finite fields, and group theory. The topics in each chapter build on one another and include extensive problem sets as well as hints to selected exercises. Key topics include walks on graphs, cubes and the Radon transform, the Matrix–Tree Theorem, and the Sperner property. There are also three appendices on purely enumerative aspects of combinatorics related to the chapter material: the RSK algorithm, plane partitions, and the enumeration of labeled trees. Richard Stanley is currently professor of Applied Mathematics at the Massachusetts Institute of Technology. Stanley has received several awards including the George Polya Prize in applied combinatorics, the Guggenheim Fellowship, and the Leroy P. Steele Prize for mathematical exposition. Also by the author: Combinatorics and Commutative Algebra, Second Edition, © Birkhauser.
| Author | : Sergey Kitaev |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 511 |
| Release | : 2011-08-30 |
| Genre | : Computers |
| ISBN | : 3642173330 |
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.
| Author | : Mark V. Sapir |
| Publisher | : Springer |
| Total Pages | : 369 |
| Release | : 2014-10-06 |
| Genre | : Mathematics |
| ISBN | : 3319080318 |
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.
| Author | : Nicholas Loehr |
| Publisher | : CRC Press |
| Total Pages | : 600 |
| Release | : 2011-02-10 |
| Genre | : Computers |
| ISBN | : 1439848866 |
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
| Author | : Miklos Bona |
| Publisher | : CRC Press |
| Total Pages | : 1073 |
| Release | : 2015-03-24 |
| Genre | : Mathematics |
| ISBN | : 1482220865 |
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
| Author | : Anders Bjorner |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 371 |
| Release | : 2006-02-25 |
| Genre | : Mathematics |
| ISBN | : 3540275967 |
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
