Ultrafilter methods in combinatorics

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Ultrafilter methods in combinatorics

Given a set X, ultrafilters determine which subsets of X 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 “B + C conjecture”.

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Mathematical subjects

Algebra and Number Theory
Discrete Mathematics and Foundations

Author(s)

Isaac Goldbring

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DOI (Digital Object Identifier)

10.14760/SNAP-2021-006-EN

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snapshot-2021-006.pdf

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