Ultrafilter methods in combinatorics

Schnappschüsse moderner Mathematik aus Oberwolfach

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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Mathematisches Fachgebiet

Algebra und Zahlentheorie
Diskrete Mathematik und Grundlagen

Autor(en)

Isaac Goldbring

Lizenz

DOI (Digital Object Identifier)

10.14760/SNAP-2021-006-EN

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snapshot-2021-006.pdf

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