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整数上的Ramsey理论（第二版）（影印版）

样章
作者：
Bruce M. Landman，Aaron Robertson
定价：
169.00元
ISBN：
978-7-04-063102-9
版面字数：
640.00千字
开本：
16开
全书页数：
暂无
装帧形式：
精装
重点项目：
暂无
出版时间：
2025-02-14
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
暂无
  • 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

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