Combinatorics, Second Edition,
Wiley
Interscience, 2003
ISBN 0-471-26296-X. Available from
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Barnes & Noble, and
Amazon.com, or as an
e-book directly from Wiley.
Table of Contents
Chapter One: The Mathematics of Choice
1.1 The Fundamental Counting Principle
1.2 Pascal's Triangle
*1.3 Elementary Probability
*1.4 Error Correcting Codes
1.5 Combinatorial Identities
1.6 Four Ways to Choose
1.7 The Binomial and Multinomial Theorems
1.8 Partitions
1.9 Elementary Symmetric Functions
*1.10 Combinatorial Algorithms
Chapter Two: The Combinatorics of Finite Functions
2.1 Stirling Numbers of the Second Kind
2.2 Bells, Balls, and Urns
2.3 The Principle of Inclusion and Exclusion
2.4 Disjoint Cycles
2.5 Stirling Numbers of the First Kind
Chapter Three: Polya's Theory of Enumeration
3.1 Function Composition
3.2 Permutation Groups
3.3 Burnside's Lemma
3.4 Symmetry Groups
3.5 Color Patterns
3.6 Polya's Theorem
3.7 The Cycle Index Polynomial
Chapter Four: Generating Functions
4.1 Difference Sequences
4.2 Ordinary Generating Functions
4.3 Applications of Generating Functions
4.4 Exponential Generating Functions
4.5 Recursive Techniques
Chapter Five: Enumeration in Graphs
5.1 The Pigeonhole Principle
*5.2 Edge Colorings and Ramsey Theory
5.3 Chromatic Polynomials
*5.4 Planar Graphs
5.5 Matching Polynomials
5.6 Oriented Graphs
5.7 Graphic Partitions
Chapter Six: Codes and Designs
6.1 Linear Codes
6.2 Decoding Algorithms
6.3 Latin Squares
6.4 Balanced Incomplete Block Designs
Appendices
A1 Symmetric Polynomials
A2 Sorting Algorithms
A3 Matrix Theory
* An asterisk indicates an optional section that can be omitted.
Reviewed, e.g., in
American Mathematical Monthly 111 (2004), 276.
Amazon.com
The author welcomes contributions to the errata
and will attempt to give appropriate recognition to the first person who
brings a mistake to his attention, e.g., via E-mail to merris@csuhayward.edu