An Introduction to Enumeration / Edition 1

An Introduction to Enumeration / Edition 1

by Alan Camina, Barry Lewis
     
 

ISBN-10: 0857295993

ISBN-13: 9780857295996

Pub. Date: 05/20/2011

Publisher: Springer London

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

Overview

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.

Product Details

ISBN-13:
9780857295996
Publisher:
Springer London
Publication date:
05/20/2011
Series:
Springer Undergraduate Mathematics Series
Edition description:
2011
Pages:
232
Product dimensions:
6.10(w) x 9.25(h) x 0.36(d)

Table of Contents

What Is Enumeration?.- Generating Functions Count.- Working with Generating Functions.- Permutation Groups.- Matrices, Sequences and Sums.- Group Actions and Counting.- Exponential Generating Functions.- Graphs.- partitions and Paths.

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