作者：(美)R.L.格拉哈姆(R.L. Gra
页数：1018页
出版社：哈尔滨工业大学出版社
出版日期：2020
ISBN：9787560386744
电子书格式：pdf/epub/txt
内容简介
本书共5部分，首部分主要包括基础图论、连通性与网络流、随机图、拟阵、超图、有限集等内容；第二部分主要包括代数表达式、渐近估计方法、终端寻找系统、拉姆塞定理等内容；第三部分主要包括与组合相关的内容；第四部分主要包括组合学在算子研究中的应用、化学中的组合学等内容；第五部分主要包括组合学的历史、组合竞赛等内容。
目录
Volume I
Preface
List of Contributors
Part I: Structures
Graphs
1. Basic Graph Theory: Paths and Circuits
2. Connectivity and Network Flows
3. Matchings and Extensions
4. Colouring, Stable Sets and Perfect Graphs
Appendix to Chapter 4: Nowhere-Zero Flows
5. Embeddings and Minors
6. Random Graphs
Finite Sets and Relations
7. Hypergraphs
8. Partially Ordered Sets
Matroids
9. Matroids: Fundamental Concepts
10. Matroid Minors
11. Matroid Optimization and Algorithms
Symmetric Structures
12. Permutation Groups
13. Finite Geometrie
14. Block Designs
15. Association Schemes
16. Codes
Combinatorial Structures in Geometry and Number Theory
17. Extremal Problems in Combinatorial Geometry
18. Convex Polytopes and Related Complexes
19. Point Lattices
20. Combinatorial Number Theory
Author Index
Subject Index
编辑手记
Volume II
Preface
List of Contributors
Part II: Aspects
21. Algebraic Enumeration
22. Asymptotic Enumeration Methods
23. Extremal Graph Theory
24. Extremal Set Systems
25. Ramsey Theory
26. Discrepancy Theory
27. Automorphism Groups, Isomorphism, Reconstruction
28. Combinatorial Optimization
29. Computational Complexity
Part III: Methods
30. Polyhedral Combinatorics
31. Tools from Linear Algebra
Appendix
32. Tools from Higher Algebra
33. Probabilistic Methods
34. Topological Methods
Part IV: Applications
35. Combinatorics in Operations Research
36. Combinatorics in Electrical Engineering and Statics
37. Combinatorics in Statistical Physics
38. Combinatorics in Chemistry
39. Applications of Combinatorics to Molecular Biology
40. Combinatorics in Computer Science
41. Combinatorics in Pure Mathematics
Part V: Horizons
42. Infinite Combinatorics
43. Combinatorial Games
44. The History of Combinatorics
Author Index
Subject Index
编辑手记
Preface
List of Contributors
Part I: Structures
Graphs
1. Basic Graph Theory: Paths and Circuits
2. Connectivity and Network Flows
3. Matchings and Extensions
4. Colouring, Stable Sets and Perfect Graphs
Appendix to Chapter 4: Nowhere-Zero Flows
5. Embeddings and Minors
6. Random Graphs
Finite Sets and Relations
7. Hypergraphs
8. Partially Ordered Sets
Matroids
9. Matroids: Fundamental Concepts
10. Matroid Minors
11. Matroid Optimization and Algorithms
Symmetric Structures
12. Permutation Groups
13. Finite Geometrie
14. Block Designs
15. Association Schemes
16. Codes
Combinatorial Structures in Geometry and Number Theory
17. Extremal Problems in Combinatorial Geometry
18. Convex Polytopes and Related Complexes
19. Point Lattices
20. Combinatorial Number Theory
Author Index
Subject Index
编辑手记
Volume II
Preface
List of Contributors
Part II: Aspects
21. Algebraic Enumeration
22. Asymptotic Enumeration Methods
23. Extremal Graph Theory
24. Extremal Set Systems
25. Ramsey Theory
26. Discrepancy Theory
27. Automorphism Groups, Isomorphism, Reconstruction
28. Combinatorial Optimization
29. Computational Complexity
Part III: Methods
30. Polyhedral Combinatorics
31. Tools from Linear Algebra
Appendix
32. Tools from Higher Algebra
33. Probabilistic Methods
34. Topological Methods
Part IV: Applications
35. Combinatorics in Operations Research
36. Combinatorics in Electrical Engineering and Statics
37. Combinatorics in Statistical Physics
38. Combinatorics in Chemistry
39. Applications of Combinatorics to Molecular Biology
40. Combinatorics in Computer Science
41. Combinatorics in Pure Mathematics
Part V: Horizons
42. Infinite Combinatorics
43. Combinatorial Games
44. The History of Combinatorics
Author Index
Subject Index
编辑手记
