Author: Miklos Bona

Publisher: CRC Press

ISBN: 1482249103

Category: Computers

Page: 534

View: 6155

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.
Read More

An Introduction to Combinatorics, Second Edition

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

Publisher: CRC Press

ISBN: 1420082612

Category: Mathematics

Page: 444

View: 4035

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.
Read More

Author: Miklos Bona

Publisher: McGraw-Hill Science/Engineering/Math

ISBN: N.A

Category: Mathematics

Page: 526

View: 3720

Written by one of the leading authors and researchers in the field, this comprehensive modern text offers a strong focus on enumeration, a vitally important area in introductory combinatorics crucial for further study in the field. Miklós Bóna's text fills the gap between introductory textbooks in discrete mathematics and advanced graduate textbooks in enumerative combinatorics, and is one of the very first intermediate-level books to focus on enumerative combinatorics. The text can be used for an advanced undergraduate course by thoroughly covering the chapters in Part I on basic enumeration and by selecting a few special topics, or for an introductory graduate course by concentrating on the main areas of enumeration discussed in Part II. The special topics of Part III make the book suitable for a reading course. This text is part of the Walter Rudin Student Series in Advanced Mathematics.
Read More

Author: Miklos Bona

Publisher: CRC Press

ISBN: 1439850526

Category: Computers

Page: 478

View: 7051

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.
Read More

Author: Robin Pemantle,Mark C. Wilson

Publisher: Cambridge University Press

ISBN: 1107031575

Category: Mathematics

Page: 380

View: 5938

This book is the result of nearly fifteen years of work on developing analytic machinery to recover, as effectively as possible, asymptotics of the coefficients of a multivariate generating function. It is the first book to describe many of the results and techniques necessary to estimate coefficients of generating functions in more than one variable.
Read More

Connecting Algebra, Combinatorics, and Geometry

Author: Emily H. Moore,Harriet Suzanne Katcher Pollatsek

Publisher: American Mathematical Soc.

ISBN: 0821891766

Category: Mathematics

Page: 298

View: 3687

Difference sets belong both to group theory and to combinatorics. Studying them requires tools from geometry, number theory, and representation theory. This book lays a foundation for these topics, including a primer on representations and characters of f
Read More

Author: Philippe Flajolet,Robert Sedgewick

Publisher: Cambridge University Press

ISBN: 1139477161

Category: Mathematics

Page: N.A

View: 6806

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.
Read More

Author: Martin Aigner

Publisher: Springer Science & Business Media

ISBN: 3540390359

Category: Mathematics

Page: 565

View: 5453

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.
Read More

Author: Martin Aigner

Publisher: Springer Science & Business Media

ISBN: 3642591019

Category: Mathematics

Page: 483

View: 3639

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
Read More

Number Theory and Cryptography, Second Edition

Author: Lawrence C. Washington

Publisher: CRC Press

ISBN: 9781420071474

Category: Mathematics

Page: 536

View: 3027

Like its bestselling predecessor, Elliptic Curves: Number Theory and Cryptography, Second Edition develops the theory of elliptic curves to provide a basis for both number theoretic and cryptographic applications. With additional exercises, this edition offers more comprehensive coverage of the fundamental theory, techniques, and applications of elliptic curves. New to the Second Edition Chapters on isogenies and hyperelliptic curves A discussion of alternative coordinate systems, such as projective, Jacobian, and Edwards coordinates, along with related computational issues A more complete treatment of the Weil and Tate–Lichtenbaum pairings Doud’s analytic method for computing torsion on elliptic curves over Q An explanation of how to perform calculations with elliptic curves in several popular computer algebra systems Taking a basic approach to elliptic curves, this accessible book prepares readers to tackle more advanced problems in the field. It introduces elliptic curves over finite fields early in the text, before moving on to interesting applications, such as cryptography, factoring, and primality testing. The book also discusses the use of elliptic curves in Fermat’s Last Theorem. Relevant abstract algebra material on group theory and fields can be found in the appendices.
Read More

Author: Miklos Bona

Publisher: CRC Press

ISBN: 1482220865

Category: Mathematics

Page: 1086

View: 9384

Presenting the state of the art, the Handbook of Enumerative Combinatorics brings together the work of today’s most prominent researchers. The contributors survey the methods of combinatorial enumeration along with the most frequent applications of these methods. This important new work is edited by Miklós Bóna of the University of Florida where he is a member of the Academy of Distinguished Teaching Scholars. He received his Ph.D. in mathematics at Massachusetts Institute of Technology in 1997. Miklós is the author of four books and more than 65 research articles, including the award-winning Combinatorics of Permutations. Miklós Bóna is an editor-in-chief for the Electronic Journal of Combinatorics and Series Editor of the Discrete Mathematics and Its Applications Series for CRC Press/Chapman and Hall. The first two chapters provide a comprehensive overview of the most frequently used methods in combinatorial enumeration, including algebraic, geometric, and analytic methods. These chapters survey generating functions, methods from linear algebra, partially ordered sets, polytopes, hyperplane arrangements, and matroids. Subsequent chapters illustrate applications of these methods for counting a wide array of objects. The contributors for this book represent an international spectrum of researchers with strong histories of results. The chapters are organized so readers advance from the more general ones, namely enumeration methods, towards the more specialized ones. Topics include coverage of asymptotic normality in enumeration, planar maps, graph enumeration, Young tableaux, unimodality, log-concavity, real zeros, asymptotic normality, trees, generalized Catalan paths, computerized enumeration schemes, enumeration of various graph classes, words, tilings, pattern avoidance, computer algebra, and parking functions. This book will be beneficial to a wide audience. It will appeal to experts on the topic interested in learning more about the finer points, readers interested in a systematic and organized treatment of the topic, and novices who are new to the field.
Read More

Multivariable Calculus

Author: Miklos Bona,Sergei Shabanov

Publisher: Orange Groove Books

ISBN: 9781616101626

Category: Mathematics

Page: 508

View: 7681

From the University of Florida Department of Mathematics, this is the third volume in a three volume presentation of calculus from a concepts perspective. The emphasis is on learning the concepts behind the theories, not the rote completion of problems.
Read More

Author: Richard P. Stanley

Publisher: Cambridge University Press

ISBN: 9780521663519

Category: Mathematics

Page: 340

View: 9956

This book is the first of a two-volume basic introduction to enumerative combinatorics at a level suitable for graduate students and research mathematicians. It concentrates on the theory and application of generating functions, a fundamental tool in enumerative combinatorics. The book covers those parts of enumerative combinatorics of greatest applicability to other areas of mathematics. The four chapters are devoted to an introduction to enumeration (suitable for advanced undergraduates), sieve methods (including the Principle of Inclusion-Exclusion), partially ordered sets, and rational generating functions. There are a large number of exercises, almost all with solutions, which greatly augment the text and provide entry into many areas not covered directly. Graduate students and research mathematicians who wish to apply combinatorics to their work will find this an authoritative reference.
Read More

Author: Terence Tao,Van H. Vu

Publisher: Cambridge University Press

ISBN: 1139458345

Category: Mathematics

Page: N.A

View: 2713

Additive combinatorics is the theory of counting additive structures in sets. This theory has seen exciting developments and dramatic changes in direction in recent years thanks to its connections with areas such as number theory, ergodic theory and graph theory. This graduate-level 2006 text will allow students and researchers easy entry into this fascinating field. Here, the authors bring together in a self-contained and systematic manner the many different tools and ideas that are used in the modern theory, presenting them in an accessible, coherent, and intuitively clear manner, and providing immediate applications to problems in additive combinatorics. The power of these tools is well demonstrated in the presentation of recent advances such as Szemerédi's theorem on arithmetic progressions, the Kakeya conjecture and Erdos distance problems, and the developing field of sum-product estimates. The text is supplemented by a large number of exercises and new results.
Read More

A Menu of Research Problems

Author: Bela Bajnok

Publisher: CRC Press

ISBN: 1351137611

Category: Mathematics

Page: 390

View: 1853

Additive Combinatorics: A Menu of Research Problems is the first book of its kind to provide readers with an opportunity to actively explore the relatively new field of additive combinatorics. The author has written the book specifically for students of any background and proficiency level, from beginners to advanced researchers. It features an extensive menu of research projects that are challenging and engaging at many different levels. The questions are new and unsolved, incrementally attainable, and designed to be approachable with various methods.
Read More

Author: Peter J. Cameron

Publisher: Cambridge University Press

ISBN: 1108417361

Category: Mathematics

Page: N.A

View: 903

Enumerative combinatorics, in its algebraic and analytic forms, is vital to many areas of mathematics, from model theory to statistical mechanics. This book, which stems from many years' experience of teaching, invites students into the subject and prepares them for more advanced texts. It is suitable as a class text or for individual study. The author provides proofs for many of the theorems to show the range of techniques available, and uses examples to link enumerative combinatorics to other areas of study. The main section of the book introduces the key tools of the subject (generating functions and recurrence relations), which are then used to study the most important combinatorial objects, namely subsets, partitions, and permutations of a set. Later chapters deal with more specialised topics, including permanents, SDRs, group actions and the Redfield-Pólya theory of cycle indices, Möbius inversion, the Tutte polynomial, and species.
Read More

Author: Herbert S. Wilf

Publisher: Elsevier

ISBN: 0080571514

Category: Mathematics

Page: 228

View: 2217

This is the Second Edition of the highly successful introduction to the use of generating functions and series in combinatorial mathematics. This new edition includes several new areas of application, including the cycle index of the symmetric group, permutations and square roots, counting polyominoes, and exact covering sequences. An appendix on using the computer algebra programs MAPLE(r) and Mathematica(r) to generate functions is also included. The book provides a clear, unified introduction to the basic enumerative applications of generating functions, and includes exercises and solutions, many new, at the end of each chapter. Key Features * Provides new applications on the cycle index of the symmetric group, permutations and square roots, counting polyominoes, and exact covering sequences * Features an Appendix on using MAPLE(r) and Mathematica (r) to generate functions * Includes many new exercises with complete solutions at the end of each chapter
Read More

Methods for Counting

Author: Carlo Mariconda,Alberto Tonolo

Publisher: Springer

ISBN: 3319030388

Category: Mathematics

Page: 665

View: 8929

This book provides an introduction to combinatorics, finite calculus, formal series, recurrences, and approximations of sums. Readers will find not only coverage of the basic elements of the subjects but also deep insights into a range of less common topics rarely considered within a single book, such as counting with occupancy constraints, a clear distinction between algebraic and analytical properties of formal power series, an introduction to discrete dynamical systems with a thorough description of Sarkovskii’s theorem, symbolic calculus, and a complete description of the Euler-Maclaurin formulas and their applications. Although several books touch on one or more of these aspects, precious few cover all of them. The authors, both pure mathematicians, have attempted to develop methods that will allow the student to formulate a given problem in a precise mathematical framework. The aim is to equip readers with a sound strategy for classifying and solving problems by pursuing a mathematically rigorous yet user-friendly approach. This is particularly useful in combinatorics, a field where, all too often, exercises are solved by means of ad hoc tricks. The book contains more than 400 examples and about 300 problems, and the reader will be able to find the proof of every result. To further assist students and teachers, important matters and comments are highlighted, and parts that can be omitted, at least during a first and perhaps second reading, are identified.
Read More

An Introduction to Enumeration and Graph Theory Fourth Edition

Author: Miklós Bóna

Publisher: World Scientific Publishing Company

ISBN: 9813148861

Category: Mathematics

Page: 616

View: 9958

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 three 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. New to this edition are the Quick Check exercises at the end of each section. In all, the new edition contains about 240 new exercises. Extra examples were added to some sections where readers asked for them. The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, the theory of designs, enumeration under group action, generating functions of labeled and unlabeled structures and algorithms and complexity. The book encourages students to learn more combinatorics, provides 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] The previous edition of this textbook has been adopted at various schools including UCLA, MIT, University of Michigan, and Swarthmore College. It was also translated into Korean.
Read More