Arithmetic progressions in sets with small sumsets

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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.
To appear in Combinatorics Probability and Computation

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Number Theory, Combinatorics, 11P70

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http://salesiana.dossiersoluciones.com/handle/123456789/74705

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0503649
 http://arxiv.org/abs/math/0503649

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arXiv