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A Walk Through Combinatorics

Author: Mikl¢s B¢na
Publisher: World Scientific
ISBN: 9814335231
Size: 35.31 MB
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Suitable for an introductory combinatorics course lasting one or two semesters, this book includes an extensive list of problems, ranging from routine exercises to research questions. It walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some the progress made in the area.

A Walk Through Combinatorics

Author: Miklós Bóna
Publisher: World Scientific Publishing Company
ISBN: 9813148861
Size: 26.62 MB
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This is a textbook for an introductory combinatorics course lasting one or two semesters. An extensive list of problems, ranging from routine exercises to research questions, is included. In each section, there are also exercises that contain material not explicitly discussed in the preceding text, so as to provide instructors with extra choices if they want to shift the emphasis of their course. Just as with the first three editions, the new edition walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some recent progress in the area: on the one hand, providing material that will help students learn the basic techniques, and on the other hand, showing that some questions at the forefront of research are comprehensible and accessible to the talented and hardworking undergraduate. The basic topics discussed are: the twelvefold way, cycles in permutations, the formula of inclusion and exclusion, the notion of graphs and trees, matchings, Eulerian and Hamiltonian cycles, and planar graphs. New to this edition are the Quick Check exercises at the end of each section. In all, the new edition contains about 240 new exercises. Extra examples were added to some sections where readers asked for them. The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, the theory of designs, enumeration under group action, generating functions of labeled and unlabeled structures and algorithms and complexity. The book encourages students to learn more combinatorics, provides them with a not only useful but also enjoyable and engaging reading. The Solution Manual is available upon request for all instructors who adopt this book as a course text. Please send your request to [email protected] The previous edition of this textbook has been adopted at various schools including UCLA, MIT, University of Michigan, and Swarthmore College. It was also translated into Korean.

An Introduction To Enumeration

Author: Alan Camina
Publisher: Springer Science & Business Media
ISBN: 9780857296009
Size: 22.97 MB
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Written for students taking a second or third year undergraduate course in mathematics or computer science, this book is the ideal companion to a course in enumeration. Enumeration is a branch of combinatorics where the fundamental subject matter is numerous methods of pattern formation and counting. Introduction to Enumeration provides a comprehensive and practical introduction to this subject giving a clear account of fundamental results and a thorough grounding in the use of powerful techniques and tools. Two major themes run in parallel through the book, generating functions and group theory. The former theme takes enumerative sequences and then uses analytic tools to discover how they are made up. Group theory provides a concise introduction to groups and illustrates how the theory can be used to count the number of symmetries a particular object has. These enrich and extend basic group ideas and techniques. The authors present their material through examples that are carefully chosen to establish key results in a natural setting. The aim is to progressively build fundamental theorems and techniques. This development is interspersed with exercises that consolidate ideas and build confidence. Some exercises are linked to particular sections while others range across a complete chapter. Throughout, there is an attempt to present key enumerative ideas in a graphic way, using diagrams to make them immediately accessible. The development assumes some basic group theory, a familiarity with analytic functions and their power series expansion along with some basic linear algebra.

Algebraic Combinatorics

Author: Richard P. Stanley
Publisher: Springer Science & Business Media
ISBN: 1461469988
Size: 39.61 MB
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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.

Introduction To Enumerative Combinatorics

Author: Miklos Bona
Publisher: McGraw-Hill Science/Engineering/Math
ISBN:
Size: 58.30 MB
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Written by one of the leading authors and researchers in the field, this comprehensive modern text offers a strong focus on enumeration, a vitally important area in introductory combinatorics crucial for further study in the field. Miklós Bóna's text fills the gap between introductory textbooks in discrete mathematics and advanced graduate textbooks in enumerative combinatorics, and is one of the very first intermediate-level books to focus on enumerative combinatorics. The text can be used for an advanced undergraduate course by thoroughly covering the chapters in Part I on basic enumeration and by selecting a few special topics, or for an introductory graduate course by concentrating on the main areas of enumeration discussed in Part II. The special topics of Part III make the book suitable for a reading course. This text is part of the Walter Rudin Student Series in Advanced Mathematics.

Combinatorics And Graph Theory

Author: John Harris
Publisher: Springer Science & Business Media
ISBN: 0387797114
Size: 37.43 MB
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These notes were first used in an introductory course team taught by the authors at Appalachian State University to advanced undergraduates and beginning graduates. The text was written with four pedagogical goals in mind: offer a variety of topics in one course, get to the main themes and tools as efficiently as possible, show the relationships between the different topics, and include recent results to convince students that mathematics is a living discipline.

A First Course In Graph Theory

Author: Gary Chartrand
Publisher: Courier Corporation
ISBN: 0486297306
Size: 20.96 MB
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Written by two prominent figures in the field, this comprehensive text provides a remarkably student-friendly approach. Its sound yet accessible treatment emphasizes the history of graph theory and offers unique examples and lucid proofs. 2004 edition.

Introductory Combinatorics

Author: Kenneth P. Bogart
Publisher: Brooks/Cole Publishing Company
ISBN: 9780121108304
Size: 30.59 MB
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Focusing on the core material of value to students in a wide variety of fields, this book presents a broad comprehensive survey of modern combinatorics at an introductory level. The author begins with an introduction of concepts fundamental to all branches of combinatorics in the context of combinatorial enumeration. Chapter 2 is devoted to enumeration problems that involve counting the number of equivalence classes of an equivalence relation. Chapter 3 discusses somewhat less direct methods of enumeration, the principle of inclusion and exclusion and generating functions. The remainder of the book is devoted to a study of combinatorial structures.

Graph Algorithms In The Language Of Linear Algebra

Author: Jeremy Kepner
Publisher: SIAM
ISBN: 9780898719918
Size: 59.19 MB
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The current exponential growth in graph data has forced a shift to parallel computing for executing graph algorithms. Implementing parallel graph algorithms and achieving good parallel performance have proven difficult. This book addresses these challenges by exploiting the well-known duality between a canonical representation of graphs as abstract collections of vertices and edges and a sparse adjacency matrix representation. This linear algebraic approach is widely accessible to scientists and engineers who may not be formally trained in computer science. The authors show how to leverage existing parallel matrix computation techniques and the large amount of software infrastructure that exists for these computations to implement efficient and scalable parallel graph algorithms. The benefits of this approach are reduced algorithmic complexity, ease of implementation, and improved performance.

A First Look At Graph Theory

Author: John Clark
Publisher: World Scientific
ISBN: 9789810204907
Size: 20.93 MB
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This book is intended to be an introductory text for mathematics and computer science students at the second and third year levels in universities. It gives an introduction to the subject with sufficient theory for students at those levels, with emphasis on algorithms and applications.