## How To Count

Author: R.B.J.T. Allenby
Publisher: CRC Press
ISBN: 1420082612
Size: 72.28 MB
Format: PDF, ePub, Mobi
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Emphasizes a Problem Solving Approach A first course in combinatorics Completely revised, How to Count: An Introduction to Combinatorics, Second Edition shows how to solve numerous classic and other interesting combinatorial problems. The authors take an easily accessible approach that introduces problems before leading into the theory involved. Although the authors present most of the topics through concrete problems, they also emphasize the importance of proofs in mathematics. New to the Second Edition This second edition incorporates 50 percent more material. It includes seven new chapters that cover occupancy problems, Stirling and Catalan numbers, graph theory, trees, Dirichlet’s pigeonhole principle, Ramsey theory, and rook polynomials. This edition also contains more than 450 exercises. Ideal for both classroom teaching and self-study, this text requires only a modest amount of mathematical background. In an engaging way, it covers many combinatorial tools, such as the inclusion-exclusion principle, generating functions, recurrence relations, and Pólya’s counting theorem.

## Introduction To Combinatorics Second Edition

Author: Walter D. Wallis
Publisher: CRC Press
ISBN: 1498777627
Size: 69.34 MB
Format: PDF, Kindle
View: 5849

What Is Combinatorics Anyway? Broadly speaking, combinatorics is the branch of mathematics dealing with different ways of selecting objects from a set or arranging objects. It tries to answer two major kinds of questions, namely, counting questions: how many ways can a selection or arrangement be chosen with a particular set of properties; and structural questions: does there exist a selection or arrangement of objects with a particular set of properties? The authors have presented a text for students at all levels of preparation. For some, this will be the first course where the students see several real proofs. Others will have a good background in linear algebra, will have completed the calculus stream, and will have started abstract algebra. The text starts by briefly discussing several examples of typical combinatorial problems to give the reader a better idea of what the subject covers. The next chapters explore enumerative ideas and also probability. It then moves on to enumerative functions and the relations between them, and generating functions and recurrences., Important families of functions, or numbers and then theorems are presented. Brief introductions to computer algebra and group theory come next. Structures of particular interest in combinatorics: posets, graphs, codes, Latin squares, and experimental designs follow. The authors conclude with further discussion of the interaction between linear algebra and combinatorics. Features Two new chapters on probability and posets. Numerous new illustrations, exercises, and problems. More examples on current technology use A thorough focus on accuracy Three appendices: sets, induction and proof techniques, vectors and matrices, and biographies with historical notes, Flexible use of MapleTM and MathematicaTM

## Introduction To Combinatorics

Author: W.D. Wallis
Publisher: CRC Press
ISBN: 1439806233
Size: 73.56 MB
Format: PDF, Mobi
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Accessible to undergraduate students, Introduction to Combinatorics presents approaches for solving counting and structural questions. It looks at how many ways a selection or arrangement can be chosen with a specific set of properties and determines if a selection or arrangement of objects exists that has a particular set of properties. To give students a better idea of what the subject covers, the authors first discuss several examples of typical combinatorial problems. They also provide basic information on sets, proof techniques, enumeration, and graph theory—topics that appear frequently throughout the book. The next few chapters explore enumerative ideas, including the pigeonhole principle and inclusion/exclusion. The text then covers enumerative functions and the relations between them. It describes generating functions and recurrences, important families of functions, and the theorems of Pólya and Redfield. The authors also present introductions to computer algebra and group theory, before considering structures of particular interest in combinatorics: graphs, codes, Latin squares, and experimental designs. The last chapter further illustrates the interaction between linear algebra and combinatorics. Exercises and problems of varying levels of difficulty are included at the end of each chapter. Ideal for undergraduate students in mathematics taking an introductory course in combinatorics, this text explores the different ways of arranging objects and selecting objects from a set. It clearly explains how to solve the various problems that arise in this branch of mathematics.

## Introduction To Combinatorial Designs Second Edition

Author: W.D. Wallis
Publisher: CRC Press
ISBN: 1584888393
Size: 35.74 MB
Format: PDF, Mobi
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Combinatorial theory is one of the fastest growing areas of modern mathematics. Focusing on a major part of this subject, Introduction to Combinatorial Designs, Second Edition provides a solid foundation in the classical areas of design theory as well as in more contemporary designs based on applications in a variety of fields. After an overview of basic concepts, the text introduces balanced designs and finite geometries. The author then delves into balanced incomplete block designs, covering difference methods, residual and derived designs, and resolvability. Following a chapter on the existence theorem of Bruck, Ryser, and Chowla, the book discusses Latin squares, one-factorizations, triple systems, Hadamard matrices, and Room squares. It concludes with a number of statistical applications of designs. Reflecting recent results in design theory and outlining several applications, this new edition of a standard text presents a comprehensive look at the combinatorial theory of experimental design. Suitable for a one-semester course or for self-study, it will prepare readers for further exploration in the field. To access supplemental materials for this volume, visit the author’s website at http://www.math.siu.edu/Wallis/designs

## Introduction To Combinatorics

Author: Martin J. Erickson
Publisher: John Wiley & Sons
ISBN: 1118637585
Size: 45.93 MB
Format: PDF, Mobi
View: 4623

Praise for the First Edition “This excellent text should prove a useful accoutrementfor any developing mathematics program . . . it’s short,it’s sweet, it’s beautifully written.”—The Mathematical Intelligencer “Erickson has prepared an exemplary work . . . stronglyrecommended for inclusion in undergraduate-level librarycollections.” —Choice Featuring a modern approach, Introduction to Combinatorics,Second Edition illustrates the applicability of combinatorialmethods and discusses topics that are not typically addressed inliterature, such as Alcuin’s sequence, Rook paths, andLeech’s lattice. The book also presents fundamentalresults, discusses interconnection and problem-solving techniques,and collects and disseminates open problems that raise questionsand observations. Many important combinatorial methods are revisited and repeatedseveral times throughout the book in exercises, examples, theorems,and proofs alike, allowing readers to build confidence andreinforce their understanding of complex material. In addition, theauthor successfully guides readers step-by-step through three majorachievements of combinatorics: Van der Waerden’s theorem onarithmetic progressions, Pólya’s graph enumerationformula, and Leech’s 24-dimensional lattice. Along withupdated tables and references that reflect recent advances invarious areas, such as error-correcting codes and combinatorialdesigns, the Second Edition also features: Many new exercises to help readers understand and applycombinatorial techniques and ideas A deeper, investigative study of combinatorics throughexercises requiring the use of computer programs Over fifty new examples, ranging in level from routine toadvanced, that illustrate important combinatorial concepts Basic principles and theories in combinatorics as well as newand innovative results in the field Introduction to Combinatorics, Second Edition is an idealtextbook for a one- or two-semester sequence in combinatorics,graph theory, and discrete mathematics at the upper-undergraduatelevel. The book is also an excellent reference for anyoneinterested in the various applications of elementarycombinatorics.

## Introduction To Enumerative And Analytic Combinatorics Second Edition

Author: Miklos Bona
Publisher: CRC Press
ISBN: 1482249103
Size: 66.98 MB
Format: PDF, Kindle
View: 5080

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 enumeration, and extremal combinatorics. Lastly, the text discusses supplemental topics, including error-correcting codes, properties of sequences, and magic squares. Strengthening the analytic flavor of the book, this Second Edition: Features a new chapter on analytic combinatorics and new sections on advanced applications of generating functions Demonstrates powerful techniques that do not require the residue theorem or complex integration Adds new exercises to all chapters, significantly extending coverage of the given topics Introduction to Enumerative and Analytic Combinatorics, Second Edition makes combinatorics more accessible, increasing interest in this rapidly expanding field.

## Applied Combinatorics Second Edition

Author: Fred Roberts
Publisher: CRC Press
ISBN: 9781420099836
Size: 24.85 MB
Format: PDF
View: 4415

Now with solutions to selected problems, Applied Combinatorics, Second Edition presents the tools of combinatorics from an applied point of view. This bestselling textbook offers numerous references to the literature of combinatorics and its applications that enable readers to delve more deeply into the topics. After introducing fundamental counting rules and the tools of graph theory and relations, the authors focus on three basic problems of combinatorics: counting, existence, and optimization problems. They discuss advanced tools for dealing with the counting problem, including generating functions, recurrences, inclusion/exclusion, and Pólya theory. The text then covers combinatorial design, coding theory, and special problems in graph theory. It also illustrates the basic ideas of combinatorial optimization through a study of graphs and networks.

## Combinatorics Second Edition

Author: Nicholas Loehr
Publisher: CRC Press
ISBN: 149878027X
Size: 47.76 MB
Format: PDF, Docs
View: 2398

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.

## Lessons In Play

Author: Michael Albert
Publisher: A K PETERS
ISBN: 9781482243031
Size: 60.67 MB
Format: PDF, Kindle
View: 3127

A thorough revision of a popular text in combinatorial game theory, this second edition reorganizes presentation to make it more widely accessible. The beginning focuses less on technical and more on conceptual material and applications. Still written in a textbook style with supporting evidence and proofs, the authors add many more exercises and examples and implement a two-step approach for some aspects of the material involving an initial introduction, examples, and basic results to be followed later by more technical and abstract results.

## A Course In Combinatorics

Author: J. H. van Lint
Publisher: Cambridge University Press
ISBN: 1139430637
Size: 43.70 MB
Format: PDF, Kindle
View: 2876

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.