Aaron Robertson

Fundamentals of Ramsey Theory (eBook, PDF)

• Format: PDF

Produktbeschreibung

This up-to-date book introduces the field of Ramsey theory from several different viewpoints. The book covers integer, graph, and Euclidean Ramsey theory with many proofs being combinatorial in nature. The author motivates topics and discussion, rather than just a list of theorems and proofs.

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Produktdetails

• Verlag: Taylor & Francis
• Seitenzahl: 255
• Erscheinungstermin: 17. Juni 2021
• Englisch
• ISBN-13: 9780429775918
• Artikelnr.: 61530946

Autorenporträt

Aaron Robertson received his Ph.D. in mathematics from Temple University under the guidance of his advisor Doron Zeilberger. Upon finishing his Ph.D. he started at Colgate University in upstate New York where he is currently Professor of Mathematics. He also serves as Associate Managing editor of the journal Integers. After a brief detour into the world of permutation patterns, he has focused most of his research on Ramsey theory.

Inhaltsangabe

1. Introduction. 1.1. What is Ramsey Theory? 1.2. Notations and
Conventions. 1.3. Prerequisites. 1.4. Compactness Principle. 1.5. Set
Theoretic Considerations. 1.6. Exercises. 2. Integer Ramsey Theory. 2.1.
Van der Waerden's Theorem. 2.2. Equations. 2.3. Hales-Jewett Theorem. 2.4.
Finite Sums. 2.5. Density Results. 2.6. Exercises. 3. Graph Ramsey Theory.
3.1. Complete Graphs. 3.2. Other Graphs. 3.3. Hypergraphs. 3.4. Infinite
Graphs. 3.5. Comparing Ramsey and van der Waerden Results. 3.6. Exercises.
4. Euclidean Ramsey Theory. 4.1. Polygons. 4.2. Chromatic Number of the
Plane. 4.3. Four Color Map Theorem. 4.4. Exercises. 5. Other Approaches to
Ramsey Theory. 5.1. Topological Approaches. 5.2. Ergodic Theory. 5.3.
Stone-¿ech Compactification. 5.4. Additive Combinatorics Methods. 5.5.
Exercises. 6. The Probabilistic Method. 6.1. Lower Bounds on Ramsey, van
der Waerden, and Hales-Jewett Numbers. 6.2. Turán's Theorem. 6.3.
Almost-surely van der Waerden and Ramsey Numbers. 6.4. Lovász Local Lemma.
6.5. Exercises. 7. Applications. 7.1. Fermat's Last Theorem. 7.2. Encoding
Information. 7.3. Data Mining. 7.4. Exercises. Bibliography. Index.