Ramsey theory on the integers 2nd Edition by Bruce Landman ISBN 978-1470438449 1470438445
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ISBN 10: 1470438445
ISBN 13: 978-1470438449
Author: Bruce M. Landman
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Table of contents:
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 of der Waerden Numbers
§2.4. Bounds on van der Waerden Numbers
§2.5. The Erdős 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 z,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 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
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Tags: Bruce Landman, Ramsey theory, the integers