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 q+3 2 directions, then either U is affinely equivalent to the graph of the function xq+1 2 or it determines at least 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
Mathematical Subject Classification 2000
Primary: 51E21
Milestones
Received: 6 February 2008
Accepted: 15 February 2008
Authors
András Gács
Tamás Szőnyi
László Lovász
Eötvös Loránd Tudományegyetem
Számítógéptudományi Tanszék
Pázmány Péter sétány 1/C
Budapest
1117
Hungary