On the directions problem in AG(n, q) |
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| Authors: | Paola De Vito |
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| Affiliation: | (1) Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy;(2) Department of Mathematics, University of Texas at Austin, Austin, TX 78712, USA; |
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| Abstract: | We prove that if q = p h , p a prime, do not exist sets U í AG(n,q){U {subseteq} AG(n,q)}, with |U| = q k and 1 < k < n, determining N directions where | fracqk - 1p - 1 < N ￡ fracq+32 q k-1+ qk-2 +...+q2 + q frac{{q^k} - 1}{p - 1} < N le frac{q+3}{2} q ^{k-1}+ q^{k-2} +dots+q{^2} + q |
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