On a two-dimensional analog of Szemeredi's Theorem in Abelian groups
Number Theory
2007-05-23 v1 Combinatorics
Abstract
Let G be a finite Abelian group and A be a subset G\times G of cardinality at least |G|^2/(log log |G|)^c, where c>0 is an absolute constant. We prove that A contains a triple {(k,m), (k+d,m), (k,m+d)}, where d does not equal 0. This theorem is a two-dimensional generalization of Szemeredi's theorem on arithmetic progressions.
Keywords
Cite
@article{arxiv.0705.0451,
title = {On a two-dimensional analog of Szemeredi's Theorem in Abelian groups},
author = {I. D. Shkredov},
journal= {arXiv preprint arXiv:0705.0451},
year = {2007}
}
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40 pages