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Aigner, Martin

A Course in Enumeration (Kartoniert / Broschiert / Paperback)

Springer Berlin Heidelberg, Springer Berlin, November 2010


Softcover reprint of hardcover 1st ed. 2007 - 576 S. - Sprache: Englisch - 236x154x32 mm Previously published in hardcover

ISBN: 3642072534 EAN: 9783642072536

Combinatorial enumeration is a readily accessible subject full of easily stated, but sometimes tantalizingly difficult problems. This book leads the reader in a leisurely way from basic notions of combinatorial enumeration to a variety of topics, ranging from algebra to statistical physics. The book is organized in three parts: Basics, Methods, and Topics. The aim is to introduce readers to a fascinating field, and to offer a sophisticated source of information for professional mathematicians desiring to learn more. There are 666 exercises, and every chapter ends with a highlight section, discussing in detail a particularly beautiful or famous result.

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Produktdetails

Combinatorial enumeration is a readily accessible subject full of easily stated, but sometimes tantalizingly difficult problems. This book leads the reader in a leisurely way from the basic notions of combinatorial enumeration to a variety of topics, ranging from algebra to statistical physics. The aim of the author is to introduce readers to a fascinating field, and to offer a sophisticated source of information for the professional mathematician who wants to learn more about the subject. The book is organized in three parts: Basics, Methods, and Topics. There are 666 exercises, and as a special feature every chapter ends with a highlight section, discussing in detail a particularly beautiful or famous result.

Inhaltsverzeichnis

Basics.- Fundamental Coefficients.- Formal Series and Infinite Matrices.- Methods.- Generating Functions.- Hypergeometric Summation.- Sieve Methods.- Enumeration of Patterns.- Topics.- The Catalan Connection.- Symmetric Functions.- Counting Polynomials.- Models from Statistical Physics.

Kritikerstimmen

From the reviews: "The goal of the text is present enumerative combinatorics together with its many applications, including chapters not common in enumerative combinatorics texts, like the ones on hypergeometric summations, on the Tutte polynomial, and on models from statistical physics. ... good number of exercises carry additional material, and a number of selected exercises are given a solution at the end. ... A nice trend in recent books - closing chapters with some spectacular 'book proofs' - is followed and will help at keeping the attention of the students." (László A. Székely, Zentralblatt MATH, Vol. 1123 (1), 2008) "The book is divided into three parts ... . the structure and topics of this book are well-designed, and there are nearly 700 exercises sprinkled throughout - many with hints and solutions in the back - which make the book far more appealing. I think it would be a good ... textbook for any graduate student wishing to learn about enumerative combinatorics." (Darren Glass, MathDL, January, 2008) "In this graduate textbook on enumerative combinatorics, the author follows the classic structure of basics-methods-special topics. ... Each chapter ends with a 'Highlight', which is a specific, high-level application of the material learned in that chapter. This will benefit instructors and interested students alike. ... the book will broaden access to several special topics and will turn them into more mainstream knowledge. The scope of the book is large, so most readers will find several sections that will teach them many facts, methods and theories." (Miklós Bóna, Mathematical Reviews, Issue 2008 f) "The techniques one needs to be an expert in enumeration are very involved, sometimes quite genius. ... This book moves this important technique much closer to the classrooms than it used to be. ... The arguments throughout the book are very clear, many exercises are presented ... . This way the lecturers with talented audience will find many ideas how to hold out the beauty behind the dry techniques. We highly recommend this book for anyone related to enumeration ... ." (Péter Hajnal, Acta Scientiarum Mathematicarum, Vol. 74, 2008) "It provides mathematical analysis of combinatorial sets ... . Martin Aigner has a reputation as a good expositor of mathematics ... and the book does not disappoint. The explanations, while often brief, are quite good. ... As the book gets more and more advanced, the explanations grow correspondingly in size. ... contains the clearest explanation of graph polynomials that I have ever found. ... the book contains good and readable expositions of an interesting and beautiful subject." (Peter Boothe, SIGACT News, Vol. 41 (2), 2010)

ISBN 3-642-07253-4

ISBN 978-3-642-07253-6

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