D. Zakharov

activity

20162026

most citedEssentially tight bounds for rainbow cycles in proper edge-colourings

3 citations · 15 across the 35 of their papers we have counts for

collaborators

Showing 2025Show all

4 papers · 1 filter

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.CO2025

A fractal-like configuration of point-line pairs for the minimal distance problem

Alexander Logunov, Dmitrii Zakharov

We show that for every $n \in N$ there is a collection of points $p_{1}, \dots, p_{n}$ and lines $ℓ_{1}, \dots, ℓ_{n}$ in the unit square such that for any $i$ we have $p_i…

math.CO2025

Heilbronn's triangle problem in three dimensions

Dominique Maldague, Hong Wang, Dmitrii Zakharov

We show that among any $n$ points in the unit cube one can find a triangle of area at most $n^{- 2/3 - c}$ for some absolute constant $c > 0$ . This gives the first non-trivial upper bo…

math.CA2025

A Continuum Beck-type Theorem for Hyperplanes

Paige Bright, Alexander Ortiz, Dmitrii Zakharov

We prove a sharp continuum Beck-type theorem for hyperplanes. Our work is inspired by foundational work of Beck on the discrete problem, as well as refinements due to Do and Lund.…

Moderate-doubling sets in F2n​ intersect subspaces

A fractal-like configuration of point-line pairs for the minimal distance problem

Heilbronn's triangle problem in three dimensions

A Continuum Beck-type Theorem for Hyperplanes

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