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Introduction to Enumerative and Analytic Combinatorics, 3 ed
◆Taylor & Francis セール開催中！：2025年9月28日(日)ご注文分まで
※上記表示の販売価格は割引適用後の価格です 出版済み 3-5週間でお届けいたします。 Series: Discrete Mathematics and Its Applications Author: Bona, Miklos (University of Florida, Gainesville, USA) Publisher: Taylor & Francis ISBN: 9781032302706 Cover: HARDCOVER Date: 2025年03月 こちらの商品は学校・法人様向け（機関契約）のオンラインブック版がございます。 オンラインブックの価格、納期につきましては弊社営業員または当ECサイトよりお問い合わせください。  DESCRIPTION This award-winning textbook targets the gap between introductory texts in discrete mathematics and advanced graduate texts in enumerative combinatorics. The author’s goal is to make combinatorics more accessible to encourage student interest and to expand the number of students studying this rapidly expanding field. 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. Updates to the Third Edition include: * Quick Check exercises at the end of each section, which are typically easier than the regular exercises at the end of each chapter. * A new section discussing the Lagrange Inversion Formula and its applications, strengthening the analytic flavor of the book. * An extended section on multivariate generating functions. Numerous exercises contain material not discussed in the text allowing instructors to extend the time they spend on a given topic. A chapter on analytic combinatorics and sections on advanced applications of generating functions, demonstrating powerful techniques that do not require the residue theorem or complex integration, and extending coverage of the given topics are highlights of the presentation. The second edition was recognized as an Outstanding Academic Title of the Year by Choice Magazine, published by the American Library Association. TABLE OF CONTENTS Basic methods When we add and when we subtract When we multiply When we divide Applications of basic counting principles The pigeonhole principle Notes Chapter review Exercises Solutions to exercises Supplementary exercises Applications of basic methods Multisets and compositions Set partitions Partitions of integers The inclusion-exclusion principle The twelvefold way Notes Chapter review Exercises Solutions to exercises Supplementary exercises Generating functions Power series Warming up: Solving recurrence relations Products of generating functions Compositions of generating functions A different type of generating functions Notes Chapter review Exercises Solutions to exercises Supplementary exercises TOPICS Counting permutations Eulerian numbers The cycle structure of permutations Cycle structure and exponential generating functions Inversions Advanced applications of generating functions to permutation enumeration Notes Chapter review Exercises Solutions to exercises Supplementary exercises Counting graphs Trees and forests Graphs and functions When the vertices are not freely labeled Graphs on colored vertices Graphs and generating functions Notes Chapter review Exercises Solutions to exercises Supplementary exercises Extremal combinatorics Extremal graph theory Hypergraphs Something is more than nothing: Existence proofs Notes Chapter review Exercises Solutions to exercises Supplementary exercises AN ADVANCED METHOD Analytic combinatorics Exponential growth rates Polynomial precision More precise asymptotics Notes Chapter review Exercises Solutions to exercises Supplementary exercises SPECIAL TOPICS Symmetric structures Designs Finite projective planes Error-correcting codes Counting symmetric structures Notes Chapter review Exercises Solutions to exercises Supplementary exercises Sequences in combinatorics Unimodality Log-concavity The real zeros property Notes Chapter review Exercises Solutions to exercises Supplementary exercises Counting magic squares and magic cubes A distribution problem Magic squares of fixed size Magic squares of fixed line sum Why magic cubes are different Notes Chapter review Exercises Solutions to exercises Supplementary exercises Appendix: The method of mathematical induction Weak induction Strong induction
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