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| 內容簡介： |
Counting problems， or more precisely enumerative combinatorics， are a source of some of the most intriguing problems in mathematics. Often these problems can be solved using ingenious and Creative observations， what we call combinatorial reasoning. It is this kind of thinking that we stress throughout the descriptions， examples， and problems in this text.
Combinatorics has many important applications to areas as diverse as computer science， probability and statistics， and discrete optimization. But equally important， the subject offers many results of beautiful mathematics that are enjoyable to discover and problems that are simply fun to think about and solve in innovative ways.
Each of us has over 40 years of experience teaching combinatorics， as well as other mathematics courses， at both the undergraduate and graduate levels. We think that we have learned some effective ways to present this subject. Early versions of the notes for the book were used in both undergraduate and graduate courses， and our students found the approach both easy to understand and quite thorough.
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PREFACE
PART I THE BASICS OF ENUMERATIVE COMBINATORICS
1 Initial EnCOUNTers with Combinatorial Reasoning
1．1 Introduction
1．2 The Pigeonhole Principle
1．3 Tiling Chessboards with Dominoes
1．4 Figurate Numbers
1．5 Counting Tilings of Rectangles
1．6 Addition and Multiplication Principles
1．7 Summary and Additional Problems
References
2 Selections， Arrangements， and Distributions
2．1 Introduction
2．2 Permutations and Combinations
2．3 Combinatorial Models
2．4 Permutations and Combinations with Repetitions
2．5 Distributions to Distinct Recipients
2．6 Circular Permutations and Derangements
2．7 Summary and Additional Problems
Reference
3 Binomial Series and Generating Functions
3．1 Introduction
3．2 The Binomial and Multinomial Theorems
3．3 Newtons Binomial Series
3．4 Ordinary Generating Functions
3．5 Exponential Generating Functions
3．6 Summary and Additional Problems
References
4 Alternating Sums， Inclusion-Exclusion Principle， Rook Polynomials， and Fibonacci Nim
4．1 Introduction
4．2 Evaluating Alternating Sums with the DIE Method
4．3 The Principle of lnclusion-Exclusion （PIE）
4．4 Rook Polynomials
4．5 （Optional）Zeckendorf Representations and Fibonacci Nim
4．6 Summary and Additional Problems
References
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PART IITWO ADDITIONAL TOPICS IN ENUMERATION
PART IIINOTATIONS INDEX， APPENDICES， AND SOLUTIONS TO SELECTED ODD PROBLEMS
Appendix
INDEX
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