COMBINATORICS OF PERMUTATIONS DISCRETE MATHEMATICS AND ITS APPLICATIONS

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Author : Miklos Bona
ISBN : 9781439850527
Genre : Computers
File Size : 37.73 MB
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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.

Author : Miklós Bóna
ISBN : 1584884347
Genre : Computers
File Size : 47.46 MB
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There are 650 articles with the word permutation in the title whose primary classification is combinatorics, but, until now, there have been no books addressing the topic. The very first book to be published on the subject, Combinatorics of Permutations contains a comprehensive, up to date treatment of the subject. Covering both enumerative and external combinatorics, this book can be used as either a graduate text or as a reference for professional mathematicians. The book includes many applications from computer science, molecular biology, probabilistic methods, and pattern avoidance, and the numerous exercises show readers a fairly comprehensive list of recent results from the field.

Author : Charalambos A. Charalambides
ISBN : 1584882905
Genre : Mathematics
File Size : 67.56 MB
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Enumerative Combinatorics presents elaborate and systematic coverage of the theory of enumeration. The first seven chapters provide the necessary background, including basic counting principles and techniques, elementary enumerative topics, and an extended presentation of generating functions and recurrence relations. The remaining seven chapters focus on more advanced topics, including, Stirling numbers, partitions of integers, partition polynomials, Eulerian numbers and Polya's counting theorem. Extensively classroom tested, this text was designed for introductory- and intermediate-level courses in enumerative combinatorics, but the far-reaching applications of the subject also make the book useful to those in operational research, the physical and social science, and anyone who uses combinatorial methods. Remarks, discussions, tables, and numerous examples support the text, and a wealth of exercises-with hints and answers provided in an appendix--further illustrate the subject's concepts, theorems, and applications.

This book was first published in 2003. Combinatorica, an extension to the popular computer algebra system Mathematica®, is the most comprehensive software available for teaching and research applications of discrete mathematics, particularly combinatorics and graph theory. This book is the definitive reference/user's guide to Combinatorica, with examples of all 450 Combinatorica functions in action, along with the associated mathematical and algorithmic theory. The authors cover classical and advanced topics on the most important combinatorial objects: permutations, subsets, partitions, and Young tableaux, as well as all important areas of graph theory: graph construction operations, invariants, embeddings, and algorithmic graph theory. In addition to being a research tool, Combinatorica makes discrete mathematics accessible in new and exciting ways to a wide variety of people, by encouraging computational experimentation and visualization. The book contains no formal proofs, but enough discussion to understand and appreciate all the algorithms and theorems it contains.

Author : Kenneth H. Rosen
ISBN : 0849301491
Genre : Mathematics
File Size : 89.72 MB
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The importance of discrete and combinatorial mathematics continues to increase as the range of applications to computer science, electrical engineering, and the biological sciences grows dramatically. Providing a ready reference for practitioners in the field, the Handbook of Discrete and Combinatorial Mathematics, Second Edition presents additional material on Google's matrix, random graphs, geometric graphs, computational topology, and other key topics. New chapters highlight essential background information on bioinformatics and computational geometry. Each chapter includes a glossary, definitions, facts, examples, algorithms, major applications, and references.

Author : V. K . Balakrishnan
ISBN : 9780486140384
Genre : Mathematics
File Size : 89.97 MB
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This concise, undergraduate-level text focuses on combinatorics, graph theory with applications to some standard network optimization problems, and algorithms. More than 200 exercises, many with complete solutions. 1991 edition.

Author : Miklos Bona
ISBN : 9781482249101
Genre : Computers
File Size : 57.81 MB
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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. Outstanding Academic Title of the Year, Choice magazine, American Library Association.

Author : Ralph P. Grimaldi
ISBN : 0201199122
Genre : Computers
File Size : 70.48 MB
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*Appropriate for four different courses: Discrete Mathematics; Combinatorics; Graph Theory; Modern Applied Algebra. *Flexible, modular organization. *This text has an enhanced mathematical approach, with carefully thought out examples, including many examples with computer sciences applications. *Carefully thought-out examples, including examples with computer science applications. Students can learn by reading the text. *The Fourth Edition has added more elementary problems, creating a larger variety of level within the problem sets which allows students to establish skills as they practice. *Chapter summaries allow the student to review what they have learned, while historical reviews and biographies bring a human element to their assignments. 1. Fundamentals of Discrete Mathematics. Fundamental Principles of Counting. The Rules of Sum and Product. Permutations. Combinations: . The Binomial Theorem. Combinations with Repetition: Distributions. An Application in the Physical Sciences (Optional). 2. Fundamentals of Logic. Basic Connectives and Truth Tables. Logical Equivalence: The Laws of Logic. Logical Implication: Rules of Inference. The Use of Quantifiers. Quantifiers, Definiti

A One-Stop Source of Known Results, a Bibliography of Papers on the Subject, and Novel Research Directions Focusing on a very active area of research in the last decade, Combinatorics of Compositions and Words provides an introduction to the methods used in the combinatorics of pattern avoidance and pattern enumeration in compositions and words. It also presents various tools and approaches that are applicable to other areas of enumerative combinatorics. After a historical perspective on research in the area, the text introduces techniques to solve recurrence relations, including iteration and generating functions. It then focuses on enumeration of basic statistics for compositions. The text goes on to present results on pattern avoidance for subword, subsequence, and generalized patterns in compositions and then applies these results to words. The authors also cover automata, the ECO method, generating trees, and asymptotic results via random compositions and complex analysis. Highlighting both established and new results, this book explores numerous tools for enumerating patterns in compositions and words. It includes a comprehensive bibliography and incorporates the use of the computer algebra systems MapleTM and Mathematica®, as well as C++ to perform computations.

Author : Thomas Koshy
ISBN : 0080477348
Genre : Mathematics
File Size : 30.32 MB
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This approachable text studies discrete objects and the relationsips that bind them. It helps students understand and apply the power of discrete math to digital computer systems and other modern applications. It provides excellent preparation for courses in linear algebra, number theory, and modern/abstract algebra and for computer science courses in data structures, algorithms, programming languages, compilers, databases, and computation. * Covers all recommended topics in a self-contained, comprehensive, and understandable format for students and new professionals * Emphasizes problem-solving techniques, pattern recognition, conjecturing, induction, applications of varying nature, proof techniques, algorithm development and correctness, and numeric computations * Weaves numerous applications into the text * Helps students learn by doing with a wealth of examples and exercises: - 560 examples worked out in detail - More than 3,700 exercises - More than 150 computer assignments - More than 600 writing projects * Includes chapter summaries of important vocabulary, formulas, and properties, plus the chapter review exercises * Features interesting anecdotes and biographies of 60 mathematicians and computer scientists * Instructor's Manual available for adopters * Student Solutions Manual available separately for purchase (ISBN: 0124211828)