E. White

activity

20182022

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Showing 2020Show all

4 papers · 1 filter

math.NT2020

On the number of distinct roots of a lacunary polynomial over finite fields

Jozsef Solymosi, Ethan P. White, Chi Hoi Yip

We obtain new upper bounds on the number of distinct roots of lacunary polynomials over finite fields. Our focus will be on polynomials for which there is a large gap between conse…

math.CO2020

Difference Necklaces

Ethan P. White, Richard K. Guy, Renate Scheidler

An $(a, b)$ -difference necklace of length $n$ is a circular arrangement of the integers $0, 1, 2, \dots, n - 1$ such that any two neighbours have absolute difference $a$ or $b$ . We…

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 $B$ …