图书信息
图书目录
整数上的Ramsey理论（第二版）（影印版）
暂无简介
作者：
Bruce M. Landman，Aaron Robertson
定价：
169.00元
出版时间：
2025-02-14
ISBN：
978-7-04-063102-9
物料号：
63102-00
读者对象：
学术著作
一级分类：
自然科学
二级分类：
数学与统计
三级分类：
组合数学与图论
重点项目：
暂无
版面字数：
640.00千字
开本：
16开
装帧形式：
精装
版次：
1
最新版次印刷时间：
2025-01-16
- 前辅文
- Preface to the Second Edition
- Acknowledgements
- Preface to the First Edition
- Chapter 1. Preliminaries
- §1.1. The Pigeonhole Principle
- §1.2. Ramsey's Theorem
- §1.3. Some Notation
- §1.4. Three Classical Theorems
- §1.5. A Little More Notation
- §1.6. Exercises
- §1.7. Research Problems
- §1.8. References
- Chapter 2. Van der Waerden's Theorem
- §2.1. The Compactness Principle
- §2.2. Alternate Forms of van der Waerden's Theorem
- §2.3. Computing van der Waerden Numbers
- §2.4. Bounds on van der Waerden Numbers
- §2.5. The Erdós and Turán Function
- §2.6. On the Number of Monochromatic Arithmetic Progressions
- §2.7. Proof of van der Waerden's Theorem
- §2.8. Exercises
- §2.9. Research Problems
- §2.10. References
- Chapter 3. Supersets of AP
- §3.1. Quasi-Progressions
- §3.2. Generalized Quasi-Progressions
- §3.3. Descending Waves
- §3.4. Semi-Progressions
- §3.5. Iterated Polynomials
- §3.6. Arithmetic Progressions as Recurrence Solutions
- §3.7. Exercises
- §3.8. Research Problems
- §3.9. References
- Chapter 4. Subsets of AP
- §4.1. Finite Gap Sets
- §4.2. Infinite Gap Sets
- §4.3. Exercises
- §4.4. Research Problems
- §4.5. References
- Chapter 5. Other Generalizations of w(k
- §5.1. Sequences of Typе x, ax+d, bx+2d
- §5.2. Homothetic Copies of Sequences
- §5.3. Sequences of Typе x, x+d, x+2d+b
- §5.4. Polynomial Progressions
- §5.5. Exercises
- §5.6. Research Problems
- §5.7. References
- Chapter 6. Arithmetic Progressions (modm)
- §6.1. The Family of Arithmetic Progressions (modm)
- §6.2. A Seemingly Smaller Family is More Regular
- §6.3. The Degree of Regularity
- §6.4. Exercises
- §6.5. Research Problems
- §6.6. References
- Chapter 7. Other Variations on van der Waerden's Theorem
- §7.1. The Function Γm(k:)
- §7.2. Monochromatic Sets a(S+6)
- §7.3. Having Most Elements Monochromatic
- §7.4. Permutations Avoiding Arithmetic Progressions
- §7.5. Exercises
- §7.6. Research Problems
- §7.7. References
- Chapter 8. Schur's Theorem
- §8.1. The Basic Theorem
- §8.2. A Generalization of Schur's Theorem
- §8.3. Refinements of Schur's Theorem
- §8.4. Schur Inequality
- §8.5. Exercises
- §8.6. Research Problems
- §8.7. References
- Chapter 9. Rado's Theorem
- §9.1. Rado's Single Equation Theorem
- §9.2. Some Rado Numbers
- §9.3. Generalizations of the Single Equation Theorem
- §9.4. Solutions to Linear Recurrences
- §9.5. Mixing Addition and Multiplication
- §9.6. Exercises
- §9.7. Research Problems
- §9.8. References
- Chapter 10. Other Topics
- §10.1. Monochromatic Sums
- §10.2. Doublefree Sets
- §10.3. Diffsequences
- §10.4. Brown's Lemma
- §10.5. Monochromatic Sets Free of Prescribed Differences
- §10.6. Patterns in Colorings
- §10.7. Rainbow Ramsey Theory on the Integers
- §10.8. Zero-Sums and m-Sets
- §10.9. Exercises
- §10.10. Research Problems
- §10.11. References
- Notation
- Bibliography
- Index
