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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.
- Sales Rank: #1747078 in Books
- Published on: 2015-10-02
- Original language: English
- Number of items: 1
- Dimensions: 9.30" h x 1.20" w x 6.30" l, 2.05 pounds
- Binding: Hardcover
- 556 pages
Review
"Miklós Bóna has done a masterful job of bringing an overview of all of enumerative combinatorics within reach of undergraduates. The two fundamental themes of bijective proofs and generating functions, together with their intimate connections, recur constantly. A wide selection of topics, including several never appearing before in a textbook, is included that gives an idea of the vast range of enumerative combinatorics. In particular, for those with sufficient background in undergraduate linear algebra and abstract algebra, there are many tantalizing hints of the fruitful connection between enumerative combinatorics and algebra that play a central role in the subject of algebraic combinatorics."
―From the Foreword to the First Edition by Richard Stanley, Cambridge, Massachusetts, USA
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.
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