Daniel Di Benedetto

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math.CO2020

Combinatorics of intervals in the plane I: trapezoids

Daniel Di Benedetto, Jozsef Solymosi, Ethan White

We study arrangements of intervals in $R^{2}$ for which many pairs form trapezoids. We show that any set of intervals forming many trapezoids must have underlying algebraic…

math.CO2020

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

Daniel Di Benedetto, Jozsef Solymosi, Ethan P. White

We prove that the number of directions contained in a set of the form $A \times B \subset A G (2, p)$ , where $p$ is prime, is at least $∣ A ∣∣ B ∣ - min {∣ A ∣, ∣ B ∣} + 2$ . Here $A$ and $B$ …