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2 claims from 1 paper

1. Mathematics › Limits and Structures in Graph Theory

   Hypergraph regularity and the multidimensional Szemerédi theorem

   Gowers · Annals of Mathematics · 2007

   The paper proves hypergraph versions of the regularity and counting lemmas, and uses them to give a combinatorial proof of the multidimensional Szemerédi theorem with an explicit bound.

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   1. UncheckedThe paper proves versions for hypergraphs of Szemerédi's regularity lemma and its counting lemma, both of which were previously known for ordinary graphs.“We prove analogues for hypergraphs of Szemerédi's regularity lemma and the associated counting lemma for graphs.”
   2. UncheckedGowers says hypergraph regularity gives the first combinatorial proof of the multidimensional Szemerédi theorem, and the first with an explicit bound.“As an application, we give the first combinatorial proof of the multidimensional Szemerédi theorem of Furstenberg and Katznelson, and the first proof that provides an explicit bound.”