An Alternate Proof of Szemer Edi's Cube Lemma Using Extremal Hypergraphs
نویسنده
چکیده
A collection H of integers is called an aane d-cube if there exist d + 1 positive) : In 1969, Szemer edi found a density result for aane cubes, namely, that for any positive integer d, there exists a constant c so that if A f1; 2; : : :; ng and jAj cn 1? 1 2 d , then A contains an aane d-cube. Using extremal hypergraphs, we ooer an entirely diierent proof of this fact (though with worse constant) which also yields a slightly stronger statement.
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