Counting sets with given doubling via dimension

Marcelo Campos, Gabriel Dahia, João Pedro Marciano

We determine, up to a factor of $2^{o(k)}$, the number of $k$-sets $A\subset \{1,\dots ,n\}$ such that $|A+A|\le m$, where $k=\Theta (\log n)$ and $m\le k^{1+\alpha }$, for small…