E. White

activity

20182022

collaborators

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6 papers · 1 filter

math.CO2022

An almost-tight $L^{2}$ autoconvolution inequality

Ethan Patrick White

Let $F$ denote the set of functions $f : [- 1/2, 1/2] \to R$ such that $\int f = 1$ . We determine the value of $in f_{f \in F} ∥ f * f ∥_{2}$ up…

math.CO2022

Erdős' minimum overlap problem

Ethan Patrick White

We obtain a substantially improved lower bound for the minimum overlap problem asked by Erdős. Our approach uses elementary Fourier analysis to translate the problem to a convex op…

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 $B$ …

math.CO2018

On rigidity of unit-bar frameworks

Jozsef Solymosi, Ethan White

We show the existence of infinitesimally rigid bipartite unit-bar frameworks in $R^{d}$ . We also construct unit-bar frameworks with girth up to 12 that are infinitesimally r…

An almost-tight L2 autoconvolution inequality

Erdős' minimum overlap problem

Difference Necklaces

Combinatorics of intervals in the plane I: trapezoids

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

On rigidity of unit-bar frameworks

An almost-tight $L^{2}$ autoconvolution inequality