Density theorems and extremal hypergraph problems

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

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