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Long arithmetic progressions in sum-sets and the number x-sum-free sets

Published online by Cambridge University Press:  25 February 2005

E. Szemerédi  and
V. H. Vu
E. Szemerédi
Affiliation:
Computer Science Department, Rutgers University, 110 Frelinghuysen Road, Piscataway, NJ 08854, USA. E-mail: [email protected]
V. H. Vu
Affiliation:
Department of Mathematics, University of California at San Diego, La Jolla, CA 92093-0112, USA. E-mail: [email protected]://www.math.ucsd.edu/~vanvu/
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Abstract

In this paper we obtain optimal bounds for the length of the longest arithmetic progression in various kinds of sum-sets. As an application, we derive a sharp estimate for the number of sets $A$ of residues modulo a prime $n$ such that no subsum of $A$ equals $x$ modulo $n$, where $x$ is a fixed residue modulo $n$.

Keywords

long arithmetic progressionsum-setFreiman inverse theoremsum-free set05A1611B2511P32
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 90 , Issue 2 , March 2005 , pp. 273 - 296
Copyright
2005 London Mathematical Society

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