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by Martin J. Erickson
Introduction to Combinatorics, 2nd Edition
Cover
Half Title page
Title page
Copyright page
Dedication
Preface
Chapter 1: Basic Counting Methods
1.1 The multiplication principle
1.2 Permutations
1.3 Combinations
1.4 Binomial coefficient identities
1.5 Distributions
1.6 The principle of inclusion and exclusion
1.7 Fibonacci numbers
1.8 Linear recurrence relations
1.9 Special recurrence relations
1.10 Counting and number theory
Notes
Chapter 2: Generating Functions
2.1 Rational generating functions
2.2 Special generating functions
2.3 Partition numbers
2.4 Labeled and unlabeled sets
2.5 Counting with symmetry
2.6 Cycle indexes
2.7 Pólya’s theorem
2.8 The number of graphs
2.9 Symmetries in domain and range
2.10 Asymmetric graphs
Notes
Chapter 3: The Pigeonhole Principle
3.1 The principle
3.2 The lattice point problem and SET®
3.3 Graphs
3.4 Colorings of the plane
3.5 Sequences and partial orders
3.6 Subsets
Notes
Chapter 4: Ramsey Theory
4.1 Ramsey’s theorem
4.2 Generalizations of Ramsey’s theorem
4.3 Ramsey numbers, bounds, and asymptotics
4.4 The probabilistic method
4.5 Schur’s theorem
4.6 Van der Waerden’s theorem
Notes
Chapter 5: Error-Correcting Codes
5.1 Binary codes
5.2 Perfect codes
5.3 Hamming codes
5.4 The Fano Configuration
Notes
Chapter 6: Combinatorial Designs
6.1 t-designs
6.2 Block designs
6.3 Projective planes
6.4 Latin squares
6.5 MOLS and OODs
6.6 Hadamard matrices
6.7 The Golay code and S(5, 8, 24)
6.8 Lattices and sphere packings
6.9 Leech’s lattice
Notes
Appendix A: Web Resources
Appendix B: Notation
Exercise Solutions
References
Index
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