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On the Number of Directions Determined by a Set of Points in an Affine Galois Plane

✍ Scribed by Tamás Szőnyi

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
265 KB
Volume
74
Category
Article
ISSN
0097-3165

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✦ Synopsis

In this paper the number of directions determined by a set of q&n points of AG(2, q) is studied. To such a set we associate a curve of degree n and show that its linear components correspond to points that can be added to the set without changing the set of determined directions. The existence of linear components is guaranteed by Weil's theorem concerning the number of GF(q)-rational points of an absolutely irreducible curve, if n is small enough.

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