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Article . 1989 . Peer-reviewed
License: Springer TDM
Data sources: Crossref
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
zbMATH Open
Article . 1989
Data sources: zbMATH Open
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Article
Data sources: DBLP
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Ultrafilters and multidimensional Ramsey Theorems

Ultrafilters and multidimensional Ramsey theorems
Authors: Vitaly Bergelson; Neil Hindman;

Ultrafilters and multidimensional Ramsey Theorems

Abstract

Simultaneous generalizations of Ramsey's theorem and single dimension Ramsey-type theorems are proved using ultrafilters on the set N of natural numbers which have certain special properties. The main result utilizes a ``combinatorically large ultrafilter'' to obtain a very strong generalization of Ramsey's theorem and Van der Waerden's theorem. Examples are given to show directions in which these results can be extended.

Related Organizations
Keywords

Combinatorial aspects of partitions of integers, Ramsey's theorem, ultrafilters

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
10
Average
Top 10%
Average
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