We present alternative proofs of density versions of some combinatorial partition theorems originally obtained by E. Szemeredi, 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. Rodl, M. Schacht, J. Skokan by extending Szemeredi's regularity lemma to hypergraphs.
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机译：我们提供了一些组合分区定理的密度形式的替代证明，这些定理最初是由E. Szemeredi，H。Furstenberg和Y. Katznelson获得的。这些证明是基于最近由W. T. Gowers和B. Nagle，V. Rodl，M. Schacht，J. Skokan独立获得的极值超图结果，方法是将Szemeredi的正则性引理扩展到超图。
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