Integer Partitions

Описание

Preface
This is a book about integer partitions. If you have never heard of this concept
before, we guess you will nevertheless be quite familiar with what it means.
For instance, in how many ways can 3 be partitioned into one or more positive
integers? Well, we can leave 3 as one part; or we can take 2 as a part and the
remaining 1 as another part; or we can have three parts of size 1. This extremely
elementary piece of mathematics shows that the answer to the question is:
"There are three integer partitions of 3."
All existing literature on partition theory is written for professionals in math-
ematics. Now when you know what integer partitions are you probably agree
with us that one should be able to study them without advanced knowledge of
mathematics. This book is intended to fill this gap in the literature.
The study of partitions has fascinated a number of great mathematicians:
Euler, Legendre, Ramanujan, Hardy, Rademacher, Sylvester, Selberg and Dyson
to name a few. They have all contributed to the development of an advanced
theory of these simple mathematical objects. In this book we start from scratch
and lead the readers step by step from the really easy stuff to unsolved research
problems. Our choice of topics was motivated by our desire to get to the meat of
the subject directly. We wanted to move quickly to one of the most magnificent
and surprising results of the entire subject, the Rogers-Ramanujan identitities.
After that we introduce enough about generating functions to enable us to touch
on the beginnings of the many fascinating aspects of the subject.
The intended audience is fairly broad. Obviously this should be the ideal
textbook for a course on partitions for undergraduates. We have tried to keep
the book to a modest length so that its topics would fit within one semester. Also
there are often people with mathematical interests who do not have an advanced
mathematics education. We hope these people will find this book tailor-made
for them. Finally we believe that anyone with basic mathematics knowledge
will find this book a solid introduction to integer partitions.

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