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Ultrafilter methods in combinatorics
Instantanés de recherche mathématique à 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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Sujet mathématique
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Algèbre et théorie des nombres
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Mathématiques discrètes et fondements des mathématiques
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DOI
10.14760/SNAP-2021-006-EN
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Mathématiques discrètes et fondements des mathématiques
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Pensées mathématiques