The number of directions determined by less than $q$ points
  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. 
Szabolcs L. Fancsali, P\'eter Sziklai and Marcella Tak\'ats
math.CO