Title: Filters in number theory and combinatorics
Language: English
Authors: Beiglböck, Mathias
Qualification level: Doctoral
Advisor: Larcher, Gerhard
Assisting Advisor: Winkler, Reinhard
Issue Date: 2004
Number of Pages: 91
Qualification level: Doctoral
Abstract: 
We are mainly concerned with certain applications of abstract topological methods to Combinatorics and Number Theory. The Stone-Cech Compactification beta S of a discrete semigroup S consists of the properly topologized set of ultrafilters on S. This structure provides surprisingly simple proofs of the Theorems of Hindman and van der Waerden. We derive new results about the algebraic structure of beta S and apply them to give different strengthenings of the Theorems mentioned above.
Some emphasis is put on Ramsey Theoretic results dealing with substructures of the positive integers which are large in an additive as well as in a multiplicative sense.

Abstract nicht verfügbar
URI: https://resolver.obvsg.at/urn:nbn:at:at-ubtuw:1-12796
http://hdl.handle.net/20.500.12708/9552
Library ID: AC04346936
Organisation: E104 - Institut für Diskrete Mathematik und Geometrie 
Publication Type: Thesis
Hochschulschrift
Appears in Collections:Thesis

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