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| 理查德 A. 布鲁迪 1964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。 .. << 查看详细 |
| 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 exercises 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 generating 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 forbidden position problem 6.6 msbius inversion 6.7 exercises chapter 7. recurrence relations and generating functions 7.1 some number sequences 7.2 linear homogeneous recurrence relations 7.3 nonhomogeneous recurrence relations 7.4 generating functions 7.5 recurrences and generating functions 7.6 a geometry example 7.7 exponential generating functions 7.8 exercises chapter 8. special counting sequences 8.1 catalan numbers 8.2 difference sequences and stirling numbers 8.3 partition numbers 8.4 a geometric problem 8.5 lattice paths and schr5der numbers 8.6 exercises chapter 9. matchings in bipartite graphs 9.1 general problem formulation 9.2 matchings 9.3 systems of distinct representatives 9.4 stable marriages 9.5 exercises chapter 10. combinatorial designs 10.1 modular arithmetic 10.2 block designs 10.3 steiner triple systems 10.4 latin squares 10.5 exercises chapter 11. introduction to graph theory 11.1 basic properties 11.2 eulerian trails 11.3 hamilton chains and cycles 11.4 bipartite multigraphs 11.5 trees 11.6 the shannon switching game 11.7 more on trees 11.8 exercises chapter 12. digraphs and networks 12.1 digraphs 12.2 networks 12.3 exercises |
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