On the directions determined by a Cartesian product in an affine Galois plane.

We prove that the number of directions contained in a set of the form $A \times B \subset AG(2,p)$, where $p$ is prime, is at least $|A||B| - \min\{|A|,|B|\} + 2$. Here $A$ and $B$ are subsets of $GF(p)$ each with at least two elements and $|A||B|

Keywords:

• Of the form
• Discrete mathematics
• Combinatorics
• Cartesian product
• Prime (order theory)
• Polynomial
• Mathematics
• Affine transformation

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