- 整数上的Ramsey理论(第2版英文版)(精)/美国数学会经典影印系列
- - 作者：(美)布鲁斯·M.兰德曼//亚伦·罗伯逊|责编:李华英
  - 出版社：高等教育
  - ISBN：9787040631029
  - 出版日期：2025/02/01
  - 页数：384
- 售价：67.6

内容大纲
Ramsey理论是对数学对象的结构的研究，这本创新的书提供了Ramsey理论对整数的第一个有凝聚力的研究。它可能包含了这个蓬勃发展的学科中已解决和未解决问题的最实质性的说明。本书适合对组合学、数论和Ramsey理论感兴趣的研究生和数学研究人员阅读参考。
作者介绍
目录
List of Tables
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 Erd?s 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 Type x,ax+d,bx+2d
  5.2.Homothetic Copies of Sequences
  5.3.Sequences of Type x,x+d,x+2d+b
  5.4.Polynomial Progressions
  5.5.Exercises
  5.6.Research Problems
  5.7.References
Chapter 6.Arithmetic Progressions (mod m)
  6.1.The Family of Arithmetic Progressions (mod m)

  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 Im(k)
  7.2.Monochromatic Sets a(S +b)
  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 Diferences
  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

内容大纲

作者介绍

目录

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