Vol. 6+7, No. 1, 2008

Download this article
Download this article For screen
For printing
Recent Issues
Volume 18
Volume 16
Volume 15
Volume 14
Volume 13
Volume 12
Volume 11
Volume 10
Volume 9
Volume 8
Volume 6+7
Volume 5
Volume 4
Volume 3
Volume 2
Volume 1
The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
ISSN (electronic): 2640-7345
ISSN (print): 2640-7337
Author Index
To Appear
Other MSP Journals
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

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.

affine planes, directions, blocking sets of Rédei type
Mathematical Subject Classification 2000
Primary: 51E21
Received: 6 February 2008
Accepted: 15 February 2008
András Gács
Tamás Szőnyi
László Lovász
Eötvös Loránd Tudományegyetem
Számítógéptudományi Tanszék
Pázmány Péter sétány 1/C