An Introduction to Enumeration

  • Alan Camina
  • Barry Lewis

Part of the Springer Undergraduate Mathematics Series book series (SUMS)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Alan Camina, Barry Lewis
    Pages 1-15
  3. Alan Camina, Barry Lewis
    Pages 17-39
  4. Alan Camina, Barry Lewis
    Pages 41-58
  5. Alan Camina, Barry Lewis
    Pages 59-78
  6. Alan Camina, Barry Lewis
    Pages 79-105
  7. Alan Camina, Barry Lewis
    Pages 107-121
  8. Alan Camina, Barry Lewis
    Pages 123-150
  9. Alan Camina, Barry Lewis
    Pages 151-175
  10. Alan Camina, Barry Lewis
    Pages 177-203
  11. Back Matter
    Pages 205-235

About this book


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. An 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.


Counting Enumeration Generating functions Group actions Groups

Authors and affiliations

  • Alan Camina
    • 1
  • Barry Lewis
    • 2
  1. 1.School of MathematicsUniversity of East AngliaNorwichUnited Kingdom
  2. 2.The Mathematical AssociationLeicesterUnited Kingdom

Bibliographic information