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Arithmetic Progressions in Sets with Small Sumsets

Published online by Cambridge University Press:  06 March 2006

JÓZSEF SOLYMOSI
JÓZSEF SOLYMOSI
Affiliation:
Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC, Canada V6T 1Z2 (e-mail: solymosi@math.ubc.ca)
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Abstract

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We present an elementary proof that if $A$ is a finite set of numbers, and the sumset $A+_GA$ is small, $|A+_GA|\leq c|A|$, along a dense graph $G$, then $A$ contains $k$-term arithmetic progressions.

Information

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 15 , Issue 4 , July 2006 , pp. 597 - 603
Copyright
2006 Cambridge University Press