Front Cover; Introduction to Combinatorics; Copyright Page; Table of Contents; Preface; Acknowledgments; Chapter 1. Introductory Examples; 1.1 A Simple Enumeration Problem; 1.2 Regions of a Plane; 1.3 Counting Labeled Trees; 1.4 Chromatic Polynomials; 1.5 Counting Hairs; 1.6 Evaluating Polynomials; 1.7 A Random Walk; Part I: ENUMERATION; Chapter 2. Permutations and Combinations; 2.1 Permutations; 2.2 r-Arrangements; 2.3 Combinations; 2.4 The Binomial Theorem; 2.5 The Binomial Coefficients; 2.6 The Multinomial Theorem; 2.7 Stirling's Formula; Chapter 3. The Inclusion-Exclusion Principle
3.1 A Calculus of Sets3.2 The Inclusion-Exclusion Principle; 3.3 Some Applications of the Inclusion-Exclusion Principle; 3.4 Derangements; Chapter 4. Linear Equations with Unit Coefficients; 4.1 Solutions Bounded Below; 4.2 Solutions Bounded Above and Below; 4.3 Combinations with Repetitions; Chapter 5. Recurrence Relations; 5.1 Recurrence Relations; 5.2 Solution by Iteration; 5.3 Difference Methods; 5.4 A Fibonacci Sequence; 5.5 A Summation Method; 5.6 Chromatic Polynomials; Chapter 6. Generating Functions; 6.1 Some Simple Examples
6.2 The Solution of Difference Equations by Means of Generating Functions6.3 Some Combinatorial Identities; 6.4 Additional Examples; 6.5 Derivatives and Differential Equations; Part II: EXISTENCE; Chapter 7. Some Methods of Proof; 7.1 Existence by Construction; 7.2 The
Method of Exhaustion; 7.3 The Dirichlet Drawer Principle; 7.4 The Method of Contradiction; Chapter 8. Geometry of the Plane; 8.1 Convex Sets; 8.2 Tiling a Rectangle; 8.3 Tessellations of the Plane; 8.4 Some Equivalence Classes; Chapter 9. Maps on a Sphere; 9.1 Euler's Formula; 9.2 Regular Maps in the Plane; 9.3 Platonic Solids
Chapter 10. Coloring Problems10.1 The Four Color Problem; 10.2 Coloring Graphs; 10.3 More about Chromatic Polynomials; 10.4 Chromatic Triangles; 10.5 Sperner's Lemma; Chapter 11. Finite Structures; 11.1 Finite Fields; 11.2 The Fano Plane; 11.3 Coordinate Geometry; 11.4 Projective Configurations; Part III: APPLICATIONS; Chapter 12. Probability; 12.1 Combinatorial Probability; 12.2 Ultimate Sets; Chapter 13. Ramifications of the Binomial Theorem; 13.1 Arithmetic Power Series; 13.2 The Binomial Distribution; 13.3 Distribution of Objects into Boxes; 13.4 Stirling Numbers
13.5 Gaussian Binomial CoefficientsChapter 14. More Generating Functions and Difference Equations; 14.1 The Partition of Integers; 14.2 Triangulation of Convex Polygons; 14.3 Random Walks; 14.4 A Class of Difference Equations; Chapter 15. Fibonacci Sequences; 15.1 Representations of Fibonacci Sequences; 15.2 Diagonal Sums of the Pascal Triangle; 15.3 Sequences of Plus and Minus Signs; 15.4 Counting Hares; 15.5 Maximum or Minimum of a Unimodal Function; Chapter 16. Arrangements; 16.1 Systems of Distinct Representatives; 16.2 Latin Squares; 16.3 The Kirkman Schoolgirl Problem