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."
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