A. Cohen

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math.CO2025

Moderate-doubling sets in $F_{2}^{n}$ intersect subspaces

Alex Cohen, Dmitrii Zakharov

We show that any set $A$ in $F_{2}^{n}$ with $∣ A + A ∣ \leq ∣ A ∣^{2 - η}$ must intersect a subspace of dimension $O_{η} (lo g ∣ A ∣)$ in at least $∣ A ∣^{η - o (1)}$ elements.

math.CO2024

Lower bounds for incidences

Alex Cohen, Cosmin Pohoata, Dmitrii Zakharov

Let $p_{1}, \dots, p_{n}$ be a set of points in the unit square and let $T_{1}, \dots, T_{n}$ be a set of $δ$ -tubes such that $T_{j}$ passes through $p_{j}$ . We prove a lower bound for the numbe…

Moderate-doubling sets in F2n​ intersect subspaces

Lower bounds for incidences

Moderate-doubling sets in $F_{2}^{n}$ intersect subspaces