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| 理查德 A.布鲁迪 19864年于美国锡拉丘兹大学获得博士学位，现为美国威斯康星大学麦迪逊分校数学系教授，曾任该系主任多年。他的研究方向包括组合数学，图论，线性代数和矩阵理论，编码理论等。布鲁迪教授的学术活动非常丰富，担任过多种学术期刊的主编。2000年由于“在组合数学研究中心所做出的杰出终身成就”而获得组合数学及其应用学会颁发的欧拉奖章。 |
| 前言 Chapter 1. What Is Combinatorics? 1.1 Example.Perfect covers of chessboards 1.2 Example.Cutting a cube 1.3 Example.Magic squares 1.4 Example.The 4-color problem 1.5 Example.The problem of the 36 officers 1.6 Example.Shortest-route problem 1.7 Example.The game of Nim 1.8 Example Chapter 2. The Pigeonhole Principle 2.1 Pigeonhole principle:Simple form 2.2 Pigeonhole principle:Strong form 2.3 A theorem of Ramsey 2.4 Exercises Chapter 3. Permutations and Combinations 3.1 Four basic counting principles 3.2 Permutations of sets 3.3 Combinations of sets 3.4 Permutations of multisets 3.5 Combinations of multisets 3.6 Exercises Chapter 4. Generating Permutations and Combinations 4.1 Generating permutations 4.2 Inversions in permutations 4.3 Inversions combinations 4.4 Generating r-combinations 4.5 Partial orders and equivalence relations 4.6 Exercises Chapter 5. The Binomial Coefficients 5.1 Pascal's formula 5.2 The binomial theorem 5.3 Identities 5.4 Unimodality of binomial coefficients 5.5 The multinomial theorem 5.6 Newton's binomial theorem 5.7 More on partially ordered sets 5.8 Exercises Chapter 6. The Inclusion-Exclusion Principle and Applications 6.1 The inclusion-exclusion principle 6.2 Combinations with repetition 6.3 Derangements 6.4 Permutations with forbidden positions 6.5 Another for bidden position problem 6.6 Mobius inversion 6.7 Exercises Chapter 7. Recurrence Relations and Generating Functions …… Chatter 8. Special Counting Sequences Chapter 9. Matchings in Bipartite Graphs Chapter 10. Combinatorial designs Chapter 11. Introduction to Graph Theory Chapter 12. Digraphs and Networks |
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