Ultrafilter methods in combinatorics

Snapshots of modern mathematics from Oberwolfach

Ultrafilter methods in combinatorics

Given a set X, ultrafilters determine which subsets of should be considered as large. We illustrate the use of ultrafilter methods in combinatorics by discussing two cornerstone results in Ramsey theory, namely Ramsey’s theorem itself and Hindman’s theorem. We then present a recent result in combinatorial number theory that verifies a conjecture of Erdős known as the “conjecture”.

If you are interested in translating this Snapshot, please contact us at info@imaginary.org

Mathematical subjects

Algebra and Number Theory
Discrete Mathematics and Foundations


Isaac Goldbring


DOI (Digital Object Identifier)


Download PDF


snapshots: overview

Mathematical subjects

Algebra and Number Theory
Didactics and Education
Discrete Mathematics and Foundations
Geometry and Topology
Numerics and Scientific Computing
Probability Theory and Statistics

Connections to other fields

Chemistry and Earth Science
Computer Science
Engineering and Technology
Humanities and Social Sciences
Life Science
Reflections on Mathematics

These icons are available under the CC BY-SA 4.0 license. Please feel free to use them to classify your own content.
The vector icons can be downloaded here.