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A Note on a Question of Erdős and Graham

Published online by Cambridge University Press:  03 March 2004

J. SOLYMOSI
J. SOLYMOSI
Affiliation:
Department of Mathematics, University of California in San Diego, 9500 Gilman Drive, La Jolla CA 92093-0112, USA (e-mail: solymosi@math.ucsd.edu) Present address: Department of Mathematics, University of British Columbia, BC, Vancouver V6T 1Y4, Canada (e-mail: solymosi@math.ubc.ca).
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Abstract

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We give a quantitative proof that, for sufficiently large $N$, every subset of $[N]^2$ of size at least $\delta N^2$ contains a square, i.e., four points with coordinates $\{(a,b),(a+d,b),(a,b+d),(a+d,b+d)\}$.

Information

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 13 , Issue 2 , March 2004 , pp. 263 - 267
Copyright
2004 Cambridge University Press