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.
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.
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.
“I loved Martin Aigner's Proofs from THE BOOK, a showcase of some
of the most elegant and appealing proofs from across mathematics,
and it has a similar feel to that. The presentations of ideas and
proofs have the kind of clarity and luminousness which makes one
feel, after reading them, that they are the natural if not the only
ones. Each chapter also ends with a 'highlight', tackling a famous
and attractive problem using the tools developed.” (Danny Yee,
dannyreviews.com, July, 2018)
“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.” (PeterBoothe, SIGACT News, Vol. 41 (2),
2010)
"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)
|
Ask a Question About this Product More... |
|
