Merris, Russell. 　著

内容

目次

Preface.Chapter 1: The Mathematics of Choice.1.1. The FundamentalCounting Principle.1.2. Pascal's Triangle.1.3. Elementary Probability.1.4.Error-Correcting Codes.1.5. Combinatorial Identities.1.6. Four Ways toChoose.1.7. The Binomial and Multinomial Theorems.1.8. Partitions.1.9.Elementary Symmetric Functions.1.10. Combinatorial Algorithms.Chapter 2: TheCombinatorics of Finite Functions.2.1. Stirling Numbers of the SecondKind.2.2. Bells, Balls, and Urns.2.3. The Principle of Inclusion andExclusion.2.4. Disjoint Cycles.2.5. Stirling Numbers of the FirstKind.Chapter 3: Polya's Theory of Enumeration.3.1. Function Composition.3.2.Permutation Groups.3.3. Burnside's Lemma.3.4. Symmetry Groups.3.5. ColorPatterns.3.6. Polya's Theorem.3.7. The Cycle Index Polynomial.Chapter 4:Generating Functions.4.1. Difference Sequences.4.2. Ordinary GeneratingFunctions.4.3. Applications of Generating Functions.4.4. ExponentialGenerating Functions.4.5. Recursive Techniques.Chapter 5: Enumeration inGraphs.5.1. The Pigeonhole Principle.5.2. Edge Colorings and RamseyTheory.5.3. Chromatic Polynomials.5.4. Planar Graphs.5.5. MatchingPolynomials.5.6. Oriented Graphs.5.7. Graphic Partitions.Chapter 6: Codes andDesigns.6.1. Linear Codes.6.2. Decoding Algorithms.6.3. Latin Squares.6.4.Balanced Incomplete Block Designs.Appendix A1: Symmetric Polynomials.AppendixA2: Sorting Algorithms.Appendix A3: Matrix Theory.Bibliography.Hints andAnswers to Selected Odd-Numbered Exercises.Index of Notation.Index.Note:Asterisks indicate optional sections that can be omitted without loss ofcontinuity.