K. O'Bryant

collaborators

Showing math.NTShow all

3 papers · 1 filter

math.NT2025

On Nathanson's Triangular Number Phenomenon

Kevin O'Bryant

For a finite set $A \subseteq Z$ , the $h$ -fold sumset is $h A := {x_{1} + \dots + x_{h} : x_{i} \in A}$ . We interpret the beginning of the sequence of sumset sizes $(∣ h A ∣)_{h = 1}^{\infty}$ …

math.NT2025

Visualizing the Sum-Product Conjecture

Kevin O'Bryant

Let $S P P (n)$ be the set ${(∣ A + A ∣, ∣ AA ∣) : A \subseteq N, ∣ A ∣ = n}$ of sum-product pairs, where $A + A$ is the sumset ${a + b : a, b \in A}$ and $AA$ is the…

math.NT2024

Bounds for Greedy $B_{h}$ -sets

Kevin O'Bryant

A set $A$ of nonnegative integers is called a $B_{h}$ -set if every solution to $a_{1} + \dots + a_{h} = b_{1} + \dots + b_{h}$ , where $a_{i}, b_{i} \in A$ , has ${a_{1}, \dots, a_{h}} = {b_{1}, \dots, b_{h}}$ (as m…

On Nathanson's Triangular Number Phenomenon

Visualizing the Sum-Product Conjecture

Bounds for Greedy Bh​-sets

Bounds for Greedy $B_{h}$ -sets