Applied Combinatorics, Second Edition

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Author: Fred Roberts,Barry Tesman

Publisher: CRC Press

ISBN: 9781420099836

Category: Computers

Page: 848

View: 1810

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.

How to Count

An Introduction to Combinatorics, Second Edition

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Author: R.B.J.T. Allenby,Alan Slomson

Publisher: CRC Press

ISBN: 1420082612

Category: Mathematics

Page: 444

View: 4092

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.

Handbook of Graph Theory, Second Edition

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Author: Jonathan L. Gross,Jay Yellen,Ping Zhang

Publisher: CRC Press

ISBN: 1439880182

Category: Mathematics

Page: 1630

View: 1595

In the ten years since the publication of the best-selling first edition, more than 1,000 graph theory papers have been published each year. Reflecting these advances, Handbook of Graph Theory, Second Edition provides comprehensive coverage of the main topics in pure and applied graph theory. This second edition—over 400 pages longer than its predecessor—incorporates 14 new sections. Each chapter includes lists of essential definitions and facts, accompanied by examples, tables, remarks, and, in some cases, conjectures and open problems. A bibliography at the end of each chapter provides an extensive guide to the research literature and pointers to monographs. In addition, a glossary is included in each chapter as well as at the end of each section. This edition also contains notes regarding terminology and notation. With 34 new contributors, this handbook is the most comprehensive single-source guide to graph theory. It emphasizes quick accessibility to topics for non-experts and enables easy cross-referencing among chapters.

Introduction to Combinatorics

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Author: Martin J. Erickson

Publisher: John Wiley & Sons

ISBN: 1118637585

Category: Mathematics

Page: 244

View: 4855

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.

Combinatorics, Second Edition

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Author: Nicholas Loehr

Publisher: CRC Press

ISBN: 149878027X

Category: Mathematics

Page: 618

View: 4013

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.

Algorithmen - Eine Einführung

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Author: Thomas H. Cormen,Charles E. Leiserson,Ronald Rivest,Clifford Stein

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110522012

Category: Computers

Page: 1339

View: 5108

Der "Cormen" bietet eine umfassende und vielseitige Einführung in das moderne Studium von Algorithmen. Es stellt viele Algorithmen Schritt für Schritt vor, behandelt sie detailliert und macht deren Entwurf und deren Analyse allen Leserschichten zugänglich. Sorgfältige Erklärungen zur notwendigen Mathematik helfen, die Analyse der Algorithmen zu verstehen. Den Autoren ist es dabei geglückt, Erklärungen elementar zu halten, ohne auf Tiefe oder mathematische Exaktheit zu verzichten. Jedes der weitgehend eigenständig gestalteten Kapitel stellt einen Algorithmus, eine Entwurfstechnik, ein Anwendungsgebiet oder ein verwandtes Thema vor. Algorithmen werden beschrieben und in Pseudocode entworfen, der für jeden lesbar sein sollte, der schon selbst ein wenig programmiert hat. Zahlreiche Abbildungen verdeutlichen, wie die Algorithmen arbeiten. Ebenfalls angesprochen werden Belange der Implementierung und andere technische Fragen, wobei, da Effizienz als Entwurfskriterium betont wird, die Ausführungen eine sorgfältige Analyse der Laufzeiten der Programme mit ein schließen. Über 1000 Übungen und Problemstellungen und ein umfangreiches Quellen- und Literaturverzeichnis komplettieren das Lehrbuch, dass durch das ganze Studium, aber auch noch danach als mathematisches Nachschlagewerk oder als technisches Handbuch nützlich ist. Für die dritte Auflage wurde das gesamte Buch aktualisiert. Die Änderungen sind vielfältig und umfassen insbesondere neue Kapitel, überarbeiteten Pseudocode, didaktische Verbesserungen und einen lebhafteren Schreibstil. So wurden etwa - neue Kapitel zu van-Emde-Boas-Bäume und mehrfädigen (engl.: multithreaded) Algorithmen aufgenommen, - das Kapitel zu Rekursionsgleichungen überarbeitet, sodass es nunmehr die Teile-und-Beherrsche-Methode besser abdeckt, - die Betrachtungen zu dynamischer Programmierung und Greedy-Algorithmen überarbeitet; Memoisation und der Begriff des Teilproblem-Graphen als eine Möglichkeit, die Laufzeit eines auf dynamischer Programmierung beruhender Algorithmus zu verstehen, werden eingeführt. - 100 neue Übungsaufgaben und 28 neue Problemstellungen ergänzt. Umfangreiches Dozentenmaterial (auf englisch) ist über die Website des US-Verlags verfügbar.

Combinatorial optimization

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Author: William Cook

Publisher: Wiley-Interscience

ISBN: 9780471558941

Category: Mathematics

Page: 355

View: 8433

A complete, highly accessible introduction to one of today's most exciting areas of applied mathematics One of the youngest, most vital areas of applied mathematics, combinatorial optimization integrates techniques from combinatorics, linear programming, and the theory of algorithms. Because of its success in solving difficult problems in areas from telecommunications to VLSI, from product distribution to airline crew scheduling, the field has seen a ground swell of activity over the past decade. Combinatorial Optimization is an ideal introduction to this mathematical discipline for advanced undergraduates and graduate students of discrete mathematics, computer science, and operations research. Written by a team of recognized experts, the text offers a thorough, highly accessible treatment of both classical concepts and recent results. The topics include: * Network flow problems * Optimal matching * Integrality of polyhedra * Matroids * NP-completeness Featuring logical and consistent exposition, clear explanations of basic and advanced concepts, many real-world examples, and helpful, skill-building exercises, Combinatorial Optimization is certain to become the standard text in the field for many years to come.

An introduction to optimization

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Author: Edwin Kah Pin Chong,Stanislaw H. Żak

Publisher: Wiley-Interscience

ISBN: N.A

Category: Mathematics

Page: 409

View: 6971

An up-to-date, accessible introduction to an increasingly important field This timely and authoritative book fills a growing need for an introductory text to optimization methods and theory at the senior undergraduate and beginning graduate levels. With consistently accessible and elementary treatment of all topics, An Introduction to Optimization helps students build a solid working knowledge of the field, including unconstrained optimization, linear programming, and constrained optimization. Supplemented with more than one hundred tables and illustrations, an extensive bibliography, and numerous worked-out examples to illustrate both theory and algorithms, this book also provides: A review of the required mathematical background material A mathematical discussion at a level accessible to MBA and business students A treatment of both linear and nonlinear programming An introduction to the most recent developments, including neural networks, genetic algorithms, and the nonsimplex method of Karmarkar A chapter on the use of descent algorithms for the training of feedforward neural networks Exercise problems after every chapter MATLAB exercises and examples An optional solutions manual with MATLAB source listings This book helps students prepare for the advanced topics and technological developments that lie ahead. It is also a useful book for researchers and professionals in mathematics, electrical engineering, economics, statistics, and business.

Optimization and Computational Logic

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Author: Kenneth McAloon,Carol Tretkoff

Publisher: Wiley-Interscience

ISBN: N.A

Category: Business & Economics

Page: 536

View: 1198

This book/software package uniquely integrates logic and operations research. Its broad coverage provides concepts, templates, and the tools for the task of attacking difficult problems which are repeatedly encountered in decision making. The first part deals with linear programming and the second with search techniques for combinatorially hard problems. The applications discussed include product mix problems, pattern recognition, classical and probabilistic logic, financial planning, and expert systems.

Cryptography, Information Theory, and Error-Correction

A Handbook for the 21st Century

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Author: Aiden A. Bruen,Mario A. Forcinito

Publisher: Wiley-Interscience

ISBN: N.A

Category: Computers

Page: 468

View: 4003

Discover the first unified treatment of today's most essentialinformation technologies— Compressing, Encrypting, andEncoding With identity theft, cybercrime, and digital file sharingproliferating in today's wired world, providing safe and accurateinformation transfers has become a paramount concern. The issuesand problems raised in this endeavor are encompassed within threedisciplines: cryptography, information theory, anderror-correction. As technology continues to develop, these fieldshave converged at a practical level, increasing the need for aunified treatment of these three cornerstones of the informationage. Stressing the interconnections of the disciplines, Cryptography,Information Theory, and Error-Correction offers a complete, yetaccessible account of the technologies shaping the 21st century.This book contains the most up-to-date, detailed, and balancedtreatment available on these subjects. The authors draw on theirexperience both in the classroom and in industry, giving the book'smaterial and presentation a unique real-world orientation. With its reader-friendly style and interdisciplinary emphasis,Cryptography, Information Theory, and Error-Correction serves asboth an admirable teaching text and a tool for self-learning. Thechapter structure allows for anyone with a high school mathematicseducation to gain a strong conceptual understanding, and provideshigher-level students with more mathematically advanced topics. Theauthors clearly map out paths through the book for readers of alllevels to maximize their learning. This book: Is suitable for courses in cryptography, information theory, orerror-correction as well as courses discussing all three areas Provides over 300 example problems with solutions Presents new and exciting algorithms adopted by industry Discusses potential applications in cell biology Details a new characterization of perfect secrecy Features in-depth coverage of linear feedback shift registers(LFSR), a staple of modern computing Follows a layered approach to facilitate discussion, withsummaries followed by more detailed explanations Provides a new perspective on the RSA algorithm Cryptography, Information Theory, and Error-Correction is anexcellent in-depth text for both graduate and undergraduatestudents of mathematics, computer science, and engineering. It isalso an authoritative overview for IT professionals, statisticians,mathematicians, computer scientists, electrical engineers,entrepreneurs, and the generally curious.

Applied and Algorithmic Graph Theory

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Author: Gary Chartrand,Ortrud R. Oellermann

Publisher: McGraw-Hill College

ISBN: 9780075571018

Category: Mathematics

Page: 395

View: 5962

Designed as a bridge to cross the gap between mathematics and computer science, and planned as the mathematics base for computer science students, this maths text is designed to help the student develop an understanding of the concept of an efficient algorithm.

Combinatorics of Permutations, Second Edition

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Author: Miklos Bona

Publisher: CRC Press

ISBN: 1439850518

Category: Computers

Page: 478

View: 4591

A Unified Account of Permutations in Modern Combinatorics A 2006 CHOICE Outstanding Academic Title, the first edition of this bestseller was lauded for its detailed yet engaging treatment of permutations. Providing more than enough material for a one-semester course, Combinatorics of Permutations, Second Edition continues to clearly show the usefulness of this subject for both students and researchers and is recommended for undergraduate libraries by the MAA. Expanded Chapters Much of the book has been significantly revised and extended. This edition includes a new section on alternating permutations and new material on multivariate applications of the exponential formula. It also discusses several important results in pattern avoidance as well as the concept of asymptotically normal distributions. New Chapter An entirely new chapter focuses on three sorting algorithms from molecular biology. This emerging area of combinatorics is known for its easily stated and extremely difficult problems, which sometimes can be solved using deep techniques from seemingly remote branches of mathematics. Additional Exercises and Problems All chapters in the second edition have more exercises and problems. Exercises are marked according to level of difficulty and many of the problems encompass results from the last eight years.

Perturbation Theory in Mathematical Programming and Its Applications

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Author: Evgenij S. Levitin

Publisher: Wiley

ISBN: 9780471939351

Category: Mathematics

Page: 402

View: 5467

Presents the author's research of local parametric optimization in the finite-dimensional case. This book provides a clear and complete formulation of the main perturbation theory problems for finite-dimensional optimization as well as new mathematical methods to analyze these problems. Using a unified approach, the author has developed a general perturbation theory for finite-dimensional extremum problems. Within the framework of this theory, methods for studying perturbed problems in zero-, first- and second-order approximations have been developed.

The Traveling Salesman Problem

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Author: E.L. Lawler,D.B. Shmoys,A.H.G. Rinnooy Kan,J.K. Lenstra

Publisher: Wiley

ISBN: N.A

Category: Computers

Page: 473

View: 3190

Provides an in-depth treatment of the Traveling Salesman problem--the archetypical problem in combinatorial optimization. Each chapter deals with a different aspect of the problem, and has been written by an acknowledged expert in the field. Focusses on the essential ideas in a self-contained manner. Includes exercises and an extensive bibliography.

Discrete location theory

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Author: Pitu B. Mirchandani

Publisher: Wiley-Interscience

ISBN: N.A

Category: Business & Economics

Page: 555

View: 2738

This invaluable resource presents the state of the art in discrete location theory. Among the topics covered are: locations with spatial interactions such as the quadratic assignment problem and competitive locations and games; duality and decomposition methods for facility location problems; the uncapacitated facility location problem; the p-median problem; location of mobile units in a stochastic environment; covering problems; and the p-center problem. Leading experts in the field of discrete location theory contributed to each chapter. In addition, there are numerous exercises, references, notes and further discussions which serve as aids for understanding theoretical and algorithmic concepts.

Knapsack problems

algorithms and computer implementations

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Author: Silvano Martello,Paolo Toth

Publisher: John Wiley & Sons

ISBN: N.A

Category: Computers

Page: 296

View: 7907

Here is a state of art examination on exact and approximate algorithms for a number of important NP-hard problems in the field of integer linear programming, which the authors refer to as ``knapsack.'' Includes not only the classical knapsack problems such as binary, bounded, unbounded or binary multiple, but also less familiar problems such as subset-sum and change-making. Well known problems that are not usually classified in the knapsack area, including generalized assignment and bin packing, are also covered. The text fully develops an algorithmic approach without losing mathematical rigor.

Produktionsfaktor Mathematik

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Author: Martin Grötschel,Klaus Lucas,Volker Mehrmann

Publisher: Springer-Verlag

ISBN: 3540894357

Category: Mathematics

Page: 480

View: 2286

Mathematik trägt immer stärker zur Produktentwicklung und Produktionssicherheit, zur Wertschöpfung und Ressourcenschonung bei. Das Buch erörtert in verschiedenen ingenieurwissenschaftlichen Themenfeldern das Verhältnis von Mathematik und Technikwissenschaften, den Beitrag der Mathematik zur industriellen Wertschöpfung und die Schlüsselrolle der Mathematik bei der Beherrschung komplexer Systeme. Gleichzeitig schlagen die Autoren Maßnahmen zur Verbesserung der Interaktion zwischen Mathematik und Technikwissenschaften, Forschung und Industrie vor.