The number of directions determined by less than $q$ points
Journal of Algebraic Combinatorics, Tome 37 (2013) no. 1, pp. 27-37.

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Summary: In this article we prove a theorem about the number of directions determined by less then q affine points, similar to the result of Blokhuis et al. (in J. Comb. Theory Ser. A $86(1)$, 187-196, 1999) on the number of directions determined by q affine points.
Keywords: projective plane, directions, polynomials
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     title = {The number of directions determined by less than $q$ points},
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Fancsali, Szabolcs L.; Sziklai, Peter; Takáts, Marcella. The number of directions determined by less than $q$ points. Journal of Algebraic Combinatorics, Tome 37 (2013) no. 1, pp. 27-37. http://geodesic.mathdoc.fr/item/JAC_2013__37_1_a6/