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组合数学 英文版PDF|Epub|txt|kindle电子书版本网盘下载
- （美）Richard A.Brusldi著 著
- 出版社： 北京：机械工业出版社
- ISBN：7111091582
- 出版时间：2002
- 标注页数：614页
- 文件大小：19MB
- 文件页数：633页
- 主题词：
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图书目录
Preface1
Chapter 1. What is Combinatorics?1
1.1 Example. Perfect covers of chessboards4
1.2 Example. Cutting a cube8
1.3 Example. Magic squares10
1.4 Example. The 4-color problem13
1.5 Example. The problem of the 36 officers14
1.6 Example. Shortest-route problem16
1.7 Example. The game of Nim18
1.8 Exercises21
2.1 Pigeonhole principle: Simple form27
Chapter 2. The Pigeonhole Principle27
2.2 Pigeonhole principle: Strong form32
2.3 A theorem of Ramsey36
2.4 Exercises41
Chapter 3. Permutations and Combinations45
3.1 Two basic counting principles45
3.2 Permutations of sets53
3.3 Combinations of Sets60
3.4 Permutations of multisets64
3.5 Combinations of multisets70
3.6 Exercises75
Chapter 4. Generating Permutations and Combinations81
4.1 Generating permutations81
4.2 Inversions in permutations87
4.3 Generating combinations93
4.5 Partial orders and equivalence relations109
4.6 Exercises116
Chapter 5. The Binomial Coefficients122
5.1 Pascal s formula122
5.2 The binomial theorem127
5.3 Identities130
5.4 Unimodality of binomial coefficients137
5.5 The multinomial theorem143
5.6 Newton s binomial theorem147
5.7 More on partially ordered sets149
5.8 Exercises152
Chapter 6. The Inclusion-Exclusion Principle and Applications159
6.1 The inclusion-exclusion principle159
6.2 Combinations with repetition168
6.3 Derangements172
6.4 Permutations with forbidden positions178
6.5 Another forbidden position problem183
6.6 Exercises185
Chapter 7. Recurrence Relations and Generating Functions190
7.1 Some number sequences191
7.2 Linear homogeneous recurrence relations202
7.3 Non-homogeneous recurrence relations213
7.4 Generating functions220
7.5 Recurrences and generating functions227
7.6 A geometry example235
7.7 Exponential generating functions240
7.8 Exercises246
Chapter 8. Special Counting Sequences252
8.1 Catalan numbers252
8.2 Difference sequences and Stirling numbrs261
8.3 Partition numbers281
8.4 A geometric problem285
8.5 Exercises290
Chapter 9. Matchings in Bipartite Graphs294
9.1 General problem formulation295
9.2 Matchings302
9.3 Systems of distinct representatives319
9.4 Stable marriages324
9.5 Exercises332
Chapter 10. Combinatorial Designs337
10.1 Modular arithmetic337
10.2 Block designs350
10.3 Steiner triple systems362
10.4 Latin squares369
10.5 Exercises393
Chapter 11. Introduction to Graph Theory400
11.1 Basic properties401
11.2 Eulerian trails412
11.3 Hamilton chains and cycles422
11.4 Bipartite multigraphs429
11.5 Trees436
11.6 The Shannon switching game443
11.7 More on trees450
11.8 Exercises463
Chapter 12. Digraphs and Networks475
12.1 Digraphs475
12.2 Networks488
12.3 Exercises496
Chapter 13. More on Graph Theory501
13.1 Chromatic number502
13.2 Plane and planar graphs514
13.3 A 5-color theorem519
13.4 Independence number and clique number523
13.5 Connectivity533
13.6 Exercises540
Chapter 14. Polya Counting546
14.1 Permutation and Symmetry groups547
14.2 Burnside s theorem559
14.3 Polya s counting formula566
14.4 Exercises586
Answers and Hints to Exercises592
Bibliography607
Index609