Introduction to Enumerative and Analytic Combinatorics (Discrete Mathematics and Its Applications) - Hardcover

Bona, Miklos

Hardcover

ISBN 10: 1032302704 ISBN 13: 9781032302706

Publisher: Chapman and Hall/CRC, 2025

Synopsis

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.

About this title

About the Author

Miklós Bóna received his Ph.D in mathematics from the Massachusetts Institute of Technology in 1997. Since 1999, he has taught at the University of Florida, where, in 2010, he was inducted into the Academy of Distinguished Teaching Scholars. Professor Bóna has mentored numerous graduate and undergraduate students. He is the author of four books and more than 65 research articles, mostly focusing on enumerative and analytic combinatorics. His book, Combinatorics of Permutations, won a 2006 Outstanding Title Award from Choice, the journal of the American Library Association. He is also an Editor-in-Chief for the Electronic Journal of Combinatorics, and for two book series at CRC Press.

Edition details

• Publisher: Chapman and Hall/CRC
• Publication date: 2025
• Language: English
• ISBN 10: 1032302704
• ISBN 13: 9781032302706
• Binding: Hardcover
• Edition number: 3
• Number of pages: 546