Overview

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. Outstanding Academic Title of the Year, Choice magazine, American Library Association.

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9781482249095

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Reviews

BA(3)naaEURO (TM)s work is a superb text for any reader learning the vast topic of combinatorics. It includes a well-written description of the fundamentals of combinatorics and several chapters of applications. Each chapter concludes with a list of important formulas available for future reference and a lengthy list of exercises. These exercises are quite comprehensive in that they include a wide range of topics, many exploring other interesting topics unexplained in the text. Most of these exercises are accompanied by complete, well-explained solutions to assist struggling readers. One of the best aspects of the book is the conversational tone in which it is written. When reading through the numerous proofs in the text, readers will feel as though they are actually in the classroom with BA(3)na (Univ. of Florida). His explanations are clear and concise, and his dry humor is both entertaining and essential to the textaEURO (TM)s development. People spreading rumors, wearing colorful hats, and embarking on hazardous vacations are much more enjoyable to count than indistinguishable balls in jars. This work is an excellent addition to the combinatorics library. --A. Misseldine, Southern Utah University

Miklos Bona 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

Author Information

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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