A Course In Combinatorics

Author : J. H. van Lint
Publisher : Cambridge University Press
ISBN 13 : 9780521006019
Total Pages : 620 pages
Book Rating : 4.15/5 ( download)

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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.

Author : Mark de Longueville
Publisher : Springer Science & Business Media
ISBN 13 : 1441979093
Total Pages : 246 pages
Book Rating : 4.94/5 ( download)

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Download or read book A Course in Topological Combinatorics written by Mark de Longueville and published by Springer Science & Business Media. This book was released on 2013 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This undergraduate textbook in topological combinatorics covers such topics as fair division, graph coloring problems, evasiveness of graph properties, and embedding problems from discrete geometry. Includes many figures and exercises.

Author : Carl G. Wagner
Publisher : American Mathematical Soc.
ISBN 13 : 1470459957
Total Pages : 272 pages
Book Rating : 4.56/5 ( download)

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Download or read book A First Course in Enumerative Combinatorics written by Carl G. Wagner and published by American Mathematical Soc.. This book was released on 2020-10-29 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: A First Course in Enumerative Combinatorics provides an introduction to the fundamentals of enumeration for advanced undergraduates and beginning graduate students in the mathematical sciences. The book offers a careful and comprehensive account of the standard tools of enumeration—recursion, generating functions, sieve and inversion formulas, enumeration under group actions—and their application to counting problems for the fundamental structures of discrete mathematics, including sets and multisets, words and permutations, partitions of sets and integers, and graphs and trees. The author's exposition has been strongly influenced by the work of Rota and Stanley, highlighting bijective proofs, partially ordered sets, and an emphasis on organizing the subject under various unifying themes, including the theory of incidence algebras. In addition, there are distinctive chapters on the combinatorics of finite vector spaces, a detailed account of formal power series, and combinatorial number theory. The reader is assumed to have a knowledge of basic linear algebra and some familiarity with power series. There are over 200 well-designed exercises ranging in difficulty from straightforward to challenging. There are also sixteen large-scale honors projects on special topics appearing throughout the text. The author is a distinguished combinatorialist and award-winning teacher, and he is currently Professor Emeritus of Mathematics and Adjunct Professor of Philosophy at the University of Tennessee. He has published widely in number theory, combinatorics, probability, decision theory, and formal epistemology. His Erdős number is 2.

Author : John Harris
Publisher : Springer Science & Business Media
ISBN 13 : 0387797114
Total Pages : 392 pages
Book Rating : 4.13/5 ( download)

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Download or read book Combinatorics and Graph Theory written by John Harris and published by Springer Science & Business Media. This book was released on 2009-04-03 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Sebastian M. Cioabă
Publisher : Springer Nature
ISBN 13 : 9811909571
Total Pages : 232 pages
Book Rating : 4.73/5 ( download)

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Download or read book A First Course in Graph Theory and Combinatorics written by Sebastian M. Cioabă and published by Springer Nature. This book was released on 2022-07-07 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the origin of graph theory from its humble beginnings in recreational mathematics to its modern setting or modeling communication networks, as is evidenced by the World Wide Web graph used by many Internet search engines. The second edition of the book includes recent developments in the theory of signed adjacency matrices involving the proof of sensitivity conjecture and the theory of Ramanujan graphs. In addition, the book discusses topics such as Pick’s theorem on areas of lattice polygons and Graham–Pollak’s work on addressing of graphs. The concept of graph is fundamental in mathematics and engineering, as it conveniently encodes diverse relations and facilitates combinatorial analysis of many theoretical and practical problems. The text is ideal for a one-semester course at the advanced undergraduate level or beginning graduate level.

Author : Jon Lee
Publisher : Cambridge University Press
ISBN 13 : 9780521010122
Total Pages : 232 pages
Book Rating : 4.28/5 ( download)

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Download or read book A First Course in Combinatorial Optimization written by Jon Lee and published by Cambridge University Press. This book was released on 2004-02-09 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained beginning graduate text covers linear and integer programming, polytopes, matroids and matroid optimization, shortest paths, and network flows.

Author : Miklós Bóna
Publisher : World Scientific Publishing Company
ISBN 13 : 9813100729
Total Pages : 568 pages
Book Rating : 4.25/5 ( download)

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Download or read book A Walk Through Combinatorics written by Miklós Bóna and published by World Scientific Publishing Company. This book was released on 2011-05-09 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 two 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. The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, the theory of designs (new to this edition), enumeration under group action (new to this edition), generating functions of labeled and unlabeled structures and algorithms and complexity. As the goal of the book is to encourage students to learn more combinatorics, every effort has been made to provide 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]. Sample Chapter(s) Chapter 1: Seven Is More Than Six. The Pigeon-Hole Principle (181 KB) Chapter 4: No Matter How You Slice It. The Binomial Theorem and Related Identities (228 KB) Chapter 15: Who Knows What It Looks Like,But It Exists. The Probabilistic Method (286 KB) Request Inspection Copy

Author : Mikl¢s B¢na
Publisher : World Scientific
ISBN 13 : 9812568859
Total Pages : 492 pages
Book Rating : 4.54/5 ( download)

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Download or read book A Walk Through Combinatorics written by Mikl¢s B¢na and published by World Scientific. This book was released on 2006 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook for an introductory combinatorics course that can take up 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 edition, 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 for the talented and hard-working 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 and Eulerian and Hamiltonian cycles. The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, and algorithms and complexity. As the goal of the book is to encourage students to learn more combinatorics, every effort has been made to provide them with a not only useful, but also enjoyable and engaging reading.

Author : Bruce E. Sagan
Publisher : American Mathematical Soc.
ISBN 13 : 1470460327
Total Pages : 304 pages
Book Rating : 4.27/5 ( download)

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Download or read book Combinatorics: The Art of Counting written by Bruce E. Sagan and published by American Mathematical Soc.. This book was released on 2020-10-16 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a gentle introduction to the enumerative part of combinatorics suitable for study at the advanced undergraduate or beginning graduate level. In addition to covering all the standard techniques for counting combinatorial objects, the text contains material from the research literature which has never before appeared in print, such as the use of quotient posets to study the Möbius function and characteristic polynomial of a partially ordered set, or the connection between quasisymmetric functions and pattern avoidance. The book assumes minimal background, and a first course in abstract algebra should suffice. The exposition is very reader friendly: keeping a moderate pace, using lots of examples, emphasizing recurring themes, and frankly expressing the delight the author takes in mathematics in general and combinatorics in particular.

Author : Philippe Flajolet
Publisher : Cambridge University Press
ISBN 13 : 1139477161
Total Pages : 825 pages
Book Rating : 4.61/5 ( download)

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Download or read book Analytic Combinatorics written by Philippe Flajolet and published by Cambridge University Press. This book was released on 2009-01-15 with total page 825 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.