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 2026Show all

6 papers · 1 filter

math.CA2026

Kakeya and Furstenberg problems for sticky sets of tubes

Hong Wang, Dmitrii Zakharov

We study incidence problems for sticky sets of tubes. In the first part, we prove a sharp Furstenberg set estimate for sticky sets of tubes in $R^{3}$ satisfying convex Wolff…

math.CA2026

Estimating the number of real zeros of linear combinations of radicals of polynomials

Gal Binyamini, Avner Kiro, Alexander Logunov +2

We obtain upper bounds for the number of real zeros of functions of the form $f (x) = k = 1 \sum n c_{k} (P_{k} (x))^{α_{k}},$ where $c_{k}, α_{k} \in R$ and each $P_k…

math.CO2026

The Erdős distinct distances problem in $R^{3}$

Jonathan Tidor, Hung-Hsun Hans Yu, Dmitrii Zakharov

We prove that $N$ points in $R^{3}$ determine at least $N^{2/3 - o (1)}$ distinct distances.

math.CO2026

Asymptotically sharp bounds for affine subspace statistics in $F_{2}^{n}$

Ting-Wei Chao, Zixuan Xu, Dmitrii Zakharov

Given a subset $A \subseteq F_{2}^{n}$ , we can consider the distribution of the intersection size of $A$ with a uniformly random $d$ -flat $F$ . Motivated by the edge statistics…

math.CO2026

Uniform Set Systems with Uniform Witnesses

Ting-Wei Chao, Zixuan Xu, Dmitrii Zakharov

Frankl--Pach and Erdős conjectured that any $(d + 1)$ -uniform set family $F \subseteq (d + 1 [ n ])$ with VC-dimension at most $d$ has size at most $(d n - 1)$ when…

math.CO2026

An isoperimetric inequality for word overlap

Dmitrii Zakharov

Let $A$ and $B$ be sets of words of length $n$ over some finite alphabet. Suppose that no suffix of a word in $A$ coincides with a prefix of a word in $B$ . Then we show that the pr…

Kakeya and Furstenberg problems for sticky sets of tubes

Estimating the number of real zeros of linear combinations of radicals of polynomials

The Erdős distinct distances problem in R3

Asymptotically sharp bounds for affine subspace statistics in F2n​

Uniform Set Systems with Uniform Witnesses

An isoperimetric inequality for word overlap

The Erdős distinct distances problem in $R^{3}$

Asymptotically sharp bounds for affine subspace statistics in $F_{2}^{n}$