Elemental methods in ergodic Ramsey theory
type: Item
instance of: scholarly article
title: Elemental methods in ergodic Ramsey theory
zbMATH Open document ID: 0945.05063
author: Randall Mccutcheon
published in: Lecture Notes in Mathematics
publication date: 2000-01-19T00:00:00Z
review text: This book gives an overview over the main results of chromatic and density Ramsey theory in \(\mathbb{Z}\). It is based on lecture notes for a graduate course and therefore additionally provides a large variety of exercises and problems that are helpful for a better understanding of the field. Even though many of the presented results were originally proven combinatorially, most of the proofs in this book are based on topological dynamics and ergodic theory. The problems considered mainly fall into the classes of van der Waerden type theorems, Hindman type theorems and Szemerédi type theorems. After an introduction to Ramsey theory and to topological dynamics in the first chapter, results from infinitary Ramsey theory and density Ramsey theory are presented in Chapters 2 and 3. In Chapters 4 and 5 ergodic theory is used to establish double recurrence results and multiple recurrence results. In particular, Roth theorems and Szeméredi theorems are proven in this context.
reviewed by: Kathrin Klamroth
Mathematics Subject Classification ID: 05D10
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 05-02
zbMATH DE Number: 1391017
zbMATH Keywords: Ramsey theory
zbMATH Keywords: topological dynamics
zbMATH Keywords: ergodic theory
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bfb0093959
OpenAlex ID: W654183047
DOI: 10.1007/BFB0093959
Recommended article: Q3784209
Recommended article: Q5490969
Recommended article: Ramsey methods in analysis
Recommended article: Elementary methods of graph Ramsey theory
Recommended article: Q4880542
Recommended article: An application of ergodic theory to a problem in geometric Ramsey theory
Recommended article: Q4011209
Recommended article: Nonstandard methods in Ramsey theory and combinatorial number theory
Recommended article: Multiplicatively large sets and ergodic Ramsey theory
Recommended article: Q5431586
description: scientific article; zbMATH DE number 1391017