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An efficient container lemma

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arxiv 1910.09208 v2 pith:K6I2UW7S submitted 2019-10-21 math.CO

An efficient container lemma

classification math.CO
keywords containercontainersefficientgeometryhypergraphstheoryallowsapproach
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We prove a new, efficient version of the hypergraph container theorems that is suited for hypergraphs with large uniformities. The main novelty is a refined approach to constructing containers that employs simple ideas from high-dimensional convex geometry. The existence of smaller families of containers for independent sets in such hypergraphs, which is guaranteed by the new theorem, allows us to improve upon the best currently known bounds for several problems in extremal graph theory, discrete geometry, and Ramsey theory.

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