Mathematics – Combinatorics
Scientific paper
2005-03-24
Mathematics
Combinatorics
25 pages, no figures, to appear, J. Combin. Thy A. This is the final version, incorporating the referee's comments
Scientific paper
Recent work of Gowers and Nagle, R\"odl, Schacht, and Skokan has established a hypergraph removal lemma, which in turn implies some results of Szemer\'edi and Furstenberg-Katznelson concerning one-dimensional and multi-dimensional arithmetic progressions respectively. In this paper we shall give a self-contained proof of this hypergraph removal lemma. In fact we prove a slight strengthening of the result, which we will use in a subsequent paper to establish infinitely many constellations of a prescribed shape in the Gaussian primes.
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