Written for students taking a second or third year undergraduate course
in mathematics or computer science, this book is the ideal companion to
a course in enumeration. Enumeration is a branch of combinatorics where
the fundamental subject matter is numerous methods of pattern formation
and counting. Introduction to Enumeration provides a comprehensive and
practical introduction to this subject giving a clear account of
fundamental results and a thorough grounding in the use of powerful
techniques and tools.
Two major themes run in parallel through the book, generating functions
and group theory. The former theme takes enumerative sequences and then
uses analytic tools to discover how they are made up. Group theory
provides a concise introduction to groups and illustrates how the theory
can be used to count the number of symmetries a particular object has.
These enrich and extend basic group ideas and techniques.
The authors present their material through examples that are carefully
chosen to establish key results in a natural setting. The aim is to
progressively build fundamental theorems and techniques. This
development is interspersed with exercises that consolidate ideas and
build confidence. Some exercises are linked to particular sections while
others range across a complete chapter. Throughout, there is an attempt
to present key enumerative ideas in a graphic way, using diagrams to
make them immediately accessible. The development assumes some basic
group theory, a familiarity with analytic functions and their power
series expansion along with some basic linear algebra.
