Download or read book Enumerative Combinatorics written by Charalambos A. Charalambides and published by CRC Press. This book was released on 2018-10-08 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Enumerative Combinatorics written by Richard Stanley and published by Springer. This book was released on 2014-11-14 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Notes on Counting An Introduction to Enumerative Combinatorics written by Peter J. Cameron and published by Cambridge University Press. This book was released on 2017-06-21 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Notes on Introductory Combinatorics written by George Pólya and published by Springer Science & Business Media. This book was released on 2009-12-02 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This is a delightful little paperback which presents a day-by-day transcription of a course taught jointly by Pólya and Tarjan at Stanford University...One can count on [Pólya and Tarjan] for new insights and a fresh outlook. Both instructors taught by presenting a succession of examples rather than by presenting a body of theory...[The book] is very well suited as supplementary material for any introductory class on combinatorics; as such, it is very highly recommended. Finally, for all of us who like the topic and delight in observing skilled professionals at work, this book is entertaining and, yes, instructive, reading." —Mathematical Reviews (Review of the original hardcover edition) "The mathematical community welcomes this book as a final contribution to honour the teacher G. Pólya." —Zentralblatt MATH (Review of the original hardcover edition)
Download or read book How to Count written by R.B.J.T. Allenby and published by CRC Press. This book was released on 2011-07-01 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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
Download or read book Introduction to Enumerative Combinatorics written by Miklós Bóna and published by McGraw-Hill Science/Engineering/Math. This book was released on 2007 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A First Course in Enumerative Combinatorics written by Carl G. Wagner and published by American Mathematical Soc.. This book was released on 2020-10-29 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: A First Course in Enumerative Combinatorics provides an introduction to the fundamentals of enumeration for advanced undergraduates and beginning graduate students in the mathematical sciences. The book offers a careful and comprehensive account of the standard tools of enumeration—recursion, generating functions, sieve and inversion formulas, enumeration under group actions—and their application to counting problems for the fundamental structures of discrete mathematics, including sets and multisets, words and permutations, partitions of sets and integers, and graphs and trees. The author's exposition has been strongly influenced by the work of Rota and Stanley, highlighting bijective proofs, partially ordered sets, and an emphasis on organizing the subject under various unifying themes, including the theory of incidence algebras. In addition, there are distinctive chapters on the combinatorics of finite vector spaces, a detailed account of formal power series, and combinatorial number theory. The reader is assumed to have a knowledge of basic linear algebra and some familiarity with power series. There are over 200 well-designed exercises ranging in difficulty from straightforward to challenging. There are also sixteen large-scale honors projects on special topics appearing throughout the text. The author is a distinguished combinatorialist and award-winning teacher, and he is currently Professor Emeritus of Mathematics and Adjunct Professor of Philosophy at the University of Tennessee. He has published widely in number theory, combinatorics, probability, decision theory, and formal epistemology. His Erdős number is 2.
Download or read book Enumerative Combinatorics Volume 2 written by Richard P. Stanley and published by Cambridge University Press. This book was released on 1997 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction, suitable for beginning graduate students, showing connections to other areas of mathematics.
Download or read book Counting The Art of Enumerative Combinatorics written by George E. Martin and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to discrete mathematics. At the end of the book the reader should be able to answer counting questions such as: How many ways are there to stack n poker chips, each of which can be red, white, blue, or green, such that each red chip is adjacent to at least 1 green chip? The book can be used as a textbook for a semester course at the sophomore level. The first five chapters can also serve as a basis for a graduate course for in-service teachers.
Download or read book A Walk Through Combinatorics written by Miklós Bóna and published by World Scientific Publishing Company. This book was released on 2006-10-09 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.
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].
Download or read book Enumerative Combinatorics Volume 1 written by Richard P. Stanley and published by Cambridge University Press. This book was released on 2011-12-12 with total page 641 pages. Available in PDF, EPUB and Kindle. Book excerpt: Richard Stanley's two-volume basic introduction to enumerative combinatorics has become the standard guide to the topic for students and experts alike. This thoroughly revised second edition of Volume 1 includes ten new sections and more than 300 new exercises, most with solutions, reflecting numerous new developments since the publication of the first edition in 1986. The author brings the coverage up to date and includes a wide variety of additional applications and examples, as well as updated and expanded chapter bibliographies. Many of the less difficult new exercises have no solutions so that they can more easily be assigned to students. The material on P-partitions has been rearranged and generalized; the treatment of permutation statistics has been greatly enlarged; and there are also new sections on q-analogues of permutations, hyperplane arrangements, the cd-index, promotion and evacuation and differential posets.
Download or read book Enumerative Combinatorics Volume 2 written by Richard P. Stanley and published by Cambridge University Press. This book was released on 1999-01-13 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second volume of a two-volume basic introduction to enumerative combinatorics covers the composition of generating functions, trees, algebraic generating functions, D-finite generating functions, noncommutative generating functions, and symmetric functions. The chapter on symmetric functions provides the only available treatment of this subject suitable for an introductory graduate course on combinatorics, and includes the important Robinson-Schensted-Knuth algorithm. Also covered are connections between symmetric functions and representation theory. An appendix by Sergey Fomin covers some deeper aspects of symmetric function theory, including jeu de taquin and the Littlewood-Richardson rule. As in Volume 1, the exercises play a vital role in developing the material. There are over 250 exercises, all with solutions or references to solutions, many of which concern previously unpublished results. Graduate students and research mathematicians who wish to apply combinatorics to their work will find this an authoritative reference.
Download or read book Handbook of Enumerative Combinatorics written by Miklos Bona and published by CRC Press. This book was released on 2015-03-24 with total page 1073 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Miklos Bona of the University of Florida where he
Download or read book Counting written by George Edward Martin and published by . This book was released on 2001 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Combinatorial Enumeration written by Ian P. Goulden and published by Courier Corporation. This book was released on 2004-06-23 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level text presents mathematical theory and problem-solving techniques associated with enumeration problems. Subjects include the combinatorics of the ordinary generating function and the exponential generating function, the combinatorics of sequences, and the combinatorics of paths. The text is complemented by approximately 350 exercises with full solutions. 1983 edition. Foreword by Gian-Carlo Rota. References. Index.
