The sum-product problem for small sets

Ginny Ray Clevenger, Haley Havard, Patch Heard +3

For $A\subseteq \mathbb{R}$, let $A+A=\{a+b:a,b\in A\}$ and $AA=\{ab:a,b\in A\}$. For $k\in \mathbb{N}$, let $SP(k)$ denote the minimum value of $\max \{|A+A|,|AA|\}$ over all $A…