Density Theorems and Extremal Hypergraph Problems

Abstract

We present alternative proofs of density versions of some combinatorial partition theorems originally obtained by H. Furstenberg and Y. Katznelson. These proofs are based on an extremal hypergraph result which was recently independently obtained by W. T. Gowers and B. Nagle, V. Rödl, M. Schacht, J. Skokan by extending Szemerédi’s regularity lemma to… (More)

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