The number of directions determined by less than $q$ points

TL;DR

This paper proves a theorem relating to the number of directions determined by fewer than q affine points, extending previous results in combinatorial geometry.

Contribution

It introduces a new theorem that generalizes earlier work on directions determined by affine points, providing insights into geometric configurations.

Findings

Established a lower bound on the number of directions for fewer than q points.

Extended previous results to a broader class of affine point sets.

Contributed to the understanding of geometric configurations in affine spaces.

Abstract

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.