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
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
Keywords: Ultrafilter; Stone-Čech-Kompaktifizierung; Halbgruppe; Zahlentheorie; Kombinatorik
URI: https://resolver.obvsg.at/urn:nbn:at:at-ubtuw:1-12796
Library ID: AC04346936
Organisation: E104 - Institut für Diskrete Mathematik und Geometrie 
Publication Type: Thesis
Appears in Collections:Thesis

Files in this item:

Show full item record

Page view(s)

checked on May 28, 2021


checked on May 28, 2021

Google ScholarTM


Items in reposiTUm are protected by copyright, with all rights reserved, unless otherwise indicated.