A variant of the hypergraph removal lemma
Terence Tao
TL;DR
This paper provides a self-contained proof of a strengthened hypergraph removal lemma, which has implications for arithmetic progressions and primes, and sets the stage for future work on prime constellations.
Contribution
It offers a new, self-contained proof of the hypergraph removal lemma and a slight strengthening of the existing result.
Findings
Self-contained proof of the hypergraph removal lemma
A strengthened version of the hypergraph removal lemma
Application to prime constellations in future work
Abstract
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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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Topology and Set Theory · Analytic Number Theory Research