On subsets of Fqn containing no k-term progressions

Authors:
Y. Lin;J. Wolf
Affiliations:
Stanford University, Department of Mathematics, Stanford, CA 94305, USA;Rutgers, The State University of New Jersey, Department of Mathematics, Piscataway, NJ 08854, USA
Venue:
European Journal of Combinatorics
Year:
2010

Citing 2
Cited 0

On subsets of finite Abelian groups with no 3-term arithmetic progressions

Journal of Combinatorial Theory Series A
Extensions of Generalized Product Caps

Designs, Codes and Cryptography

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Abstract

In this paper we prove that for any fixed integer k and any prime power q=k, there exists a subset of F"q^2^k of size q^2^(^k^-^1^)+q^k^-^1-1 which contains no k points on a line, and hence no k-term arithmetic progressions. As a corollary we obtain an asymptotic lower bound as n-~ for r"k(F"q^n) when q=k, which can be interpreted as the finite field analogue of Behrend's construction for longer progressions.