Author

João Pedro Marciano

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Preprint Sep 2026

Counting sets with given doubling via dimension

We determine, up to a factor of $2^{o(k)}$, the number of $k$-sets $A \subset \{1, \ldots, n\}$ such that $|A + A| \leq m$, where $k = \Theta(\log n)$ and $m \leq k^{1 + \alpha}$, for small $\alpha>0$, answering a question of Green and Morris.

Marcelo Campos, Gabriel Dahia, João Pedro Marciano · 0 citations

Preprint Jul 2026

Dense sets without large sumsets

We prove, for all fixed $0<\delta<1$, and all sufficiently large $n$, that there exists $S \subset [n]$ with $|S| \ge \delta n$ such that $A + B \not \subset S$ for all ${A, B \subset \mathbb{N}}$ satisfying $$\min\big\{|A|, |B|\big\} \ge \big(3 + o(1)\big) \frac{\log n }{ \log (1 / \delta)}.$$ A very recent result of...

Gabriel Dahia, João Pedro Marciano, Victor Souza · 0 citations