Dylan A. King

activity

20172026

most citedLarge Sets with Small Injective Projections

2 citations · 2 across the 7 of their papers we have counts for

collaborators

7 papers

math.CO2026

$1$ -cross intersecting set pair systems are small

Dylan King, Van Magnan, Cory Palmer

A set pair system ${(A_{i}, B_{i})}_{i = 1}^{m}$ is $1$ -cross intersecting if $∣ A_{i} \cap B_{i} ∣ = 0$ for all $i$ and $∣ A_{i} \cap B_{j} ∣ = 1$ whenever $i \neq = j$ . Let $m (a, b, 1)$ denote the maximu…

cs.DS2026

The online monotone array completion problem

Vishesh Jain, Dylan King, Clayton Mizgerd

Consider the following online filling game. An array of length $n$ is initially empty. At each time step one observes an independent sample from $Unif [0, 1]$ and must eithe…

math.NT2020

Generalizing the Distribution of Missing Sums in Sumsets

Hung V. Chu, Dylan King, Noah Luntzlara +5

Given a finite set of integers $A$ , its sumset is $A + A := {a_{i} + a_{j} ∣ a_{i}, a_{j} \in A}$ . We examine $∣ A + A ∣$ as a random variable, where $A \subset I_{n} = [0, n - 1]$ , the set of integer…

math.FA2020

Extensions of Autocorrelation Inequalities with Applications to Additive Combinatorics

Sara Fish, Dylan King, Steven J. Miller

In a 2019 paper, Barnard and Steinerberger show that for $f \in L^{1} (R)$ , the following autocorrelation inequality holds: \begin{equation*} \min_{0 \leq t \leq 1} \int_\math…

math.CO2019

Crescent configurations in normed spaces

Sara Fish, Dylan King, Steven J. Miller +2

We study the problem of crescent configurations, posed by Erdős in 1989. A crescent configuration is a set of $n$ points in the plane such that: 1) no three points lie on a common…

math.MG2019★ 2 cited

Large Sets with Small Injective Projections

Frank Coen, Nate Gillman, Tamás Keleti +2

Let $ℓ_{1}, ℓ_{2}, \dots$ be a countable collection of lines in $R^{d}$ . For any $t \in [0, 1]$ we construct a compact set $Γ \subset R^{d}$ with Hausdorff dimension $…

math.SP2017

Spectral Decimation for Families of Self-Similar Symmetric Laplacians on the Sierpinski Gasket

Sizhen Fang, Dylan A. King, Eun Bi Lee +1

We construct a one-parameter family of Laplacians on the Sierpinski Gasket that are symmetric and self-similar for the 9-map iterated function system obtained by iterating the stan…