ON THE NUMBER OF DIRECTIONS DETERMINED BY A SET OF POINTS IN AN AFFINE GALOIS PLANE

Authors
SZONYI T
Citation
T. Szonyi, ON THE NUMBER OF DIRECTIONS DETERMINED BY A SET OF POINTS IN AN AFFINE GALOIS PLANE, J COMB TH A, 74(1), 1996, pp. 141-146
Citations number
8
Categorie Soggetti
Mathematics, Pure",Mathematics
Journal title
JOURNAL OF COMBINATORIAL THEORY SERIES A
ISSN journal
00973165 → ACNP
Volume
74
Issue
1
Year of publication
1996
Pages
141 - 146
Database
ISI
SICI code
0097-3165(1996)74:1<141:OTNODD>2.0.ZU;2-J
Abstract
In this paper the number of directions determined by a set of q-n poin ts of AG(2, q) is studied. To such a set we associate a curve of degre e it and show that its linear components correspond to points that can be added to the set: without changing the set of determined direction s. The existence of linear components is guaranteed by Well's theorem concerning the number of GF(q)-rational points of an absolutely irredu cible curve, if it is small enough. (C) 1996 Academic Press, Inc.