#### Vol. 6+7, No. 1, 2008

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Directions in $\mathsf{AG}(2,p^2)$

### András Gács, Tamás Szőnyi and László Lovász

Vol. 6+7 (2008), No. 1, 189–201
DOI: 10.2140/iig.2008.6.189
##### Abstract

In this paper we prove that if $q$ is the square of a prime and $U$ is a set of $q$ points determining at least $\frac{q+3}{2}$ directions, then either $U$ is affinely equivalent to the graph of the function ${x}^{\frac{q+1}{2}}$ or it determines at least $\frac{q+p}{2}+1$ directions. This is sharp, the example is due to Polverino, Szőnyi and Weiner. Our method combines the lacunary polynomial and the double power sum approach.

##### Keywords
affine planes, directions, blocking sets of Rédei type
Primary: 51E21