K. O'Bryant

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20242026

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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.NT2024

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…