Ultrafilter methods in combinatorics
오버불파크에서 찍은 현대수학의 면모
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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