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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
版面字数：
640千字
开本：
16开
装帧形式：
精装
版次：
1
最新版次
印刷时间：
2025年
ISBN：
978-7-04-063102-9
物料号：
63102-00
出版时间：
2025-02-14
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
  • 目录
    • 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;r)
                                                                              • §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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