论文信息 - Hypergraph regularity and the multidimensional Szemerédi theorem

Hypergraph regularity and the multidimensional Szemerédi theorem

We prove analogues for hypergraphs of Szemeredi's regularity lemma and the associated counting lemma for graphs. As an application, we give the first combinatorial proof of the multidimensional Szemeredi theorem of Furstenberg and Katznelson, and the first proof that provides an explicit bound. Similar results with the same consequences have been obtained independently by Nagle, Rodl, Schacht and Skokan.

W. T. Gowers | W. Gowers

[1] K. F. Roth. On Certain Sets of Integers , 1953 .

[2] E. Szemerédi. Regular Partitions of Graphs , 1975 .

[3] H. Furstenberg,et al. An ergodic Szemerédi theorem for commuting transformations , 1978 .

[4] D. Ornstein,et al. The ergodic theoretical proof of Szemerédi's theorem , 1982 .

[5] W. T. Gowers,et al. A new proof of Szemerédi's theorem , 2001 .

[6] W. T. Gowers,et al. A NEW PROOF OF SZEMER ´ EDI'S THEOREM , 2001 .

[7] J. Solymosi. Note on a Generalization of Roth’s Theorem , 2003 .

[8] Vojtech Rödl,et al. Regularity Lemma for k‐uniform hypergraphs , 2004, Random Struct. Algorithms.

[9] Ilya D. Shkredov,et al. On a problem of Gowers , 2006 .

[10] W. T. Gowers,et al. Quasirandomness, Counting and Regularity for 3-Uniform Hypergraphs , 2006, Combinatorics, Probability and Computing.

[11] Terence Tao. A variant of the hypergraph removal lemma , 2006, J. Comb. Theory, Ser. A.

[12] V. Rödl,et al. The counting lemma for regular k-uniform hypergraphs , 2006 .