Walk Through Combinatorics A An Introduction To Enumeration And Graph Theory Third Edition

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Walk Through Combinatorics, A: An Introduction To Enumeration And Graph Theory (Third Edition)

Author : Miklos Bona
Publisher : World Scientific Publishing Company
ISBN 13 : 9813100729
Total Pages : 567 pages
Book Rating : 4.8/5 (131 download)

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Book Synopsis Walk Through Combinatorics, A: An Introduction To Enumeration And Graph Theory (Third Edition) by : Miklos Bona

Download or read book Walk Through Combinatorics, A: An Introduction To Enumeration And Graph Theory (Third Edition) written by Miklos Bona and published by World Scientific Publishing Company. This book was released on 2011-05-09 with total page 567 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].

A Walk Through Combinatorics

Author : Mikl¢s B¢na
Publisher : World Scientific
ISBN 13 : 9812568859
Total Pages : 492 pages
Book Rating : 4.8/5 (125 download)

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Book Synopsis A Walk Through Combinatorics by : Mikl¢s B¢na

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.

A Course in Combinatorics

Author : J. H. van Lint
Publisher : Cambridge University Press
ISBN 13 : 9780521006019
Total Pages : 620 pages
Book Rating : 4.0/5 (6 download)

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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.

Combinatorics

Author : Nicholas Loehr
Publisher : CRC Press
ISBN 13 : 149878027X
Total Pages : 849 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis Combinatorics by : Nicholas Loehr

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 849 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.

Combinatorics

Author : Peter Jephson Cameron
Publisher : Cambridge University Press
ISBN 13 : 9780521457613
Total Pages : 372 pages
Book Rating : 4.4/5 (576 download)

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Book Synopsis Combinatorics by : Peter Jephson Cameron

Download or read book Combinatorics written by Peter Jephson Cameron and published by Cambridge University Press. This book was released on 1994-10-06 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorics is a subject of increasing importance because of its links with computer science, statistics, and algebra. This textbook stresses common techniques (such as generating functions and recursive construction) that underlie the great variety of subject matter, and the fact that a constructive or algorithmic proof is more valuable than an existence proof. The author emphasizes techniques as well as topics and includes many algorithms described in simple terms. The text should provide essential background for students in all parts of discrete mathematics.

Introduction to Enumerative and Analytic Combinatorics

Author : Miklos Bona
Publisher : CRC Press
ISBN 13 : 1482249103
Total Pages : 555 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Introduction to Enumerative and Analytic Combinatorics by : Miklos Bona

Download or read book Introduction to Enumerative and Analytic Combinatorics written by Miklos Bona and published by CRC Press. This book was released on 2015-09-18 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Enumerative and Analytic Combinatorics fills the gap between introductory texts in discrete mathematics and advanced graduate texts in enumerative combinatorics. The book first deals with basic counting principles, compositions and partitions, and generating functions. It then focuses on the structure of permutations, graph enumerat

Introduction to Combinatorics

Author : Martin J. Erickson
Publisher : John Wiley & Sons
ISBN 13 : 1118030893
Total Pages : 210 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Introduction to Combinatorics by : Martin J. Erickson

Download or read book Introduction to Combinatorics written by Martin J. Erickson and published by John Wiley & Sons. This book was released on 2011-10-24 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: This gradual, systematic introduction to the main concepts of combinatorics is the ideal text for advanced undergraduate and early graduate courses in this subject. Each of the book's three sections--Existence, Enumeration, and Construction--begins with a simply stated first principle, which is then developed step by step until it leads to one of the three major achievements of combinatorics: Van der Waerden's theorem on arithmetic progressions, Polya's graph enumeration formula, and Leech's 24-dimensional lattice. Along the way, Professor Martin J. Erickson introduces fundamental results, discusses interconnection and problem-solving techniques, and collects and disseminates open problems that raise new and innovative questions and observations. His carefully chosen end-of-chapter exercises demonstrate the applicability of combinatorial methods to a wide variety of problems, including many drawn from the William Lowell Putnam Mathematical Competition. Many important combinatorial methods are revisited several times in the course of the text--in exercises and examples as well as theorems and proofs. This repetition enables students to build confidence and reinforce their understanding of complex material. Mathematicians, statisticians, and computer scientists profit greatly from a solid foundation in combinatorics. Introduction to Combinatorics builds that foundation in an orderly, methodical, and highly accessible manner.

Constructive Combinatorics

Author : Dennis Stanton
Publisher : Springer Science & Business Media
ISBN 13 : 1461249686
Total Pages : 194 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Constructive Combinatorics by : Dennis Stanton

Download or read book Constructive Combinatorics written by Dennis Stanton and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notes that eventually became this book were written between 1977 and 1985 for the course called Constructive Combinatorics at the University of Minnesota. This is a one-quarter (10 week) course for upper level undergraduate students. The class usually consists of mathematics and computer science majors, with an occasional engineering student. Several graduate students in computer science also attend. At Minnesota, Constructive Combinatorics is the third quarter of a three quarter sequence. The fIrst quarter, Enumerative Combinatorics, is at the level of the texts by Bogart [Bo], Brualdi [Br], Liu [Li] or Tucker [Tu] and is a prerequisite for this course. The second quarter, Graph Theory and Optimization, is not a prerequisite. We assume that the students are familiar with the techniques of enumeration: basic counting principles, generating functions and inclusion/exclusion. This course evolved from a course on combinatorial algorithms. That course contained a mixture of graph algorithms, optimization and listing algorithms. The computer assignments generally consisted of testing algorithms on examples. While we felt that such material was useful and not without mathematical content, we did not think that the course had a coherent mathematical focus. Furthermore, much of it was being taught, or could have been taught, elsewhere. Graph algorithms and optimization, for instance, were inserted into the graph theory course where they naturally belonged. The computer science department already taught some of the material: the simpler algorithms in a discrete mathematics course; effIciency of algorithms in a more advanced course.

Combinatorics and Graph Theory

Author : John Harris
Publisher : Springer Science & Business Media
ISBN 13 : 0387797114
Total Pages : 392 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Combinatorics and Graph Theory by : John Harris

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.

Combinatorics: The Art of Counting

Author : Bruce E. Sagan
Publisher : American Mathematical Soc.
ISBN 13 : 1470460327
Total Pages : 304 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Combinatorics: The Art of Counting by : Bruce E. Sagan

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.

A First Course in Graph Theory and Combinatorics

Author : Sebastian M. Cioabă
Publisher : Springer Nature
ISBN 13 : 9811909571
Total Pages : 232 pages
Book Rating : 4.8/5 (119 download)

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Book Synopsis A First Course in Graph Theory and Combinatorics by : Sebastian M. Cioabă

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.

Introductory Combinatorics

Author : Kenneth P. Bogart
Publisher : Harcourt Brace College Publishers
ISBN 13 :
Total Pages : 648 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Introductory Combinatorics by : Kenneth P. Bogart

Download or read book Introductory Combinatorics written by Kenneth P. Bogart and published by Harcourt Brace College Publishers. This book was released on 1990 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introductory, Combinatorics, Third Edition is designed for introductory courses in combinatorics, or more generally, discrete mathematics. The author, Kenneth Bogart, has chosen core material of value to students in a wide variety of disciplines: mathematics, computer science, statistics, operations research, physical sciences, and behavioral sciences. The rapid growth in the breadth and depth of the field of combinatorics in the last several decades, first in graph theory and designs and more recently in enumeration and ordered sets, has led to a recognition of combinatorics as a field with which the aspiring mathematician should become familiar. This long-overdue new edition of a popular set presents a broad comprehensive survey of modern combinatorics which is important to the various scientific fields of study.

Analytic Combinatorics

Author : Philippe Flajolet
Publisher : Cambridge University Press
ISBN 13 : 1139477161
Total Pages : 825 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Analytic Combinatorics by : Philippe Flajolet

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.

A Course in Enumeration

Author : Martin Aigner
Publisher : Springer Science & Business Media
ISBN 13 : 3540390359
Total Pages : 568 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis A Course in Enumeration by : Martin Aigner

Download or read book A Course in Enumeration written by Martin Aigner and published by Springer Science & Business Media. This book was released on 2007-06-28 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial enumeration is a readily accessible subject full of easily stated, but sometimes tantalizingly difficult problems. This book leads the reader in a leisurely way from basic notions of combinatorial enumeration to a variety of topics, ranging from algebra to statistical physics. The book is organized in three parts: Basics, Methods, and Topics. The aim is to introduce readers to a fascinating field, and to offer a sophisticated source of information for professional mathematicians desiring to learn more. There are 666 exercises, and every chapter ends with a highlight section, discussing in detail a particularly beautiful or famous result.

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

Extremal Combinatorics

Author : Stasys Jukna
Publisher : Springer Science & Business Media
ISBN 13 : 3662046504
Total Pages : 389 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Extremal Combinatorics by : Stasys Jukna

Download or read book Extremal Combinatorics written by Stasys Jukna and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a concise, up-to-date introduction to extremal combinatorics for non-specialists. Strong emphasis is made on theorems with particularly elegant and informative proofs which may be called the gems of the theory. A wide spectrum of the most powerful combinatorial tools is presented, including methods of extremal set theory, the linear algebra method, the probabilistic method and fragments of Ramsey theory. A thorough discussion of recent applications to computer science illustrates the inherent usefulness of these methods.

Combinatorics

Author : Pavle Mladenović
Publisher : Springer
ISBN 13 : 3030008312
Total Pages : 372 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Combinatorics by : Pavle Mladenović

Download or read book Combinatorics written by Pavle Mladenović and published by Springer. This book was released on 2019-03-13 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides a theoretical background for several topics in combinatorial mathematics, such as enumerative combinatorics (including partitions and Burnside's lemma), magic and Latin squares, graph theory, extremal combinatorics, mathematical games and elementary probability. A number of examples are given with explanations while the book also provides more than 300 exercises of different levels of difficulty that are arranged at the end of each chapter, and more than 130 additional challenging problems, including problems from mathematical olympiads. Solutions or hints to all exercises and problems are included. The book can be used by secondary school students preparing for mathematical competitions, by their instructors, and by undergraduate students. The book may also be useful for graduate students and for researchers that apply combinatorial methods in different areas.