Visualizing the Sum-Product Conjecture

Kevin O'Bryant

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