Introduction to Enumerative and Analytic Combinatorics

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.