D. Zakharov

activity

20242026

collaborators

4 papers

math.CO2026

Cutting corners

Andrey Kupavskii, Arsenii Sagdeev, Dmitrii Zakharov

We say that a subset $M$ of $R^{n}$ is exponentially Ramsey if there are $I^µ > 0$ and $n_{0}$ such that $I ¨ (R^{n}, M) \geq (1 + I^µ)^{n}$ for any $n > n_{0}$ , where $I ¨ (R^{n}, M)$ …

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.…

math.CO2024

Sharp bounds for rainbow matchings in hypergraphs

Cosmin Pohoata, Lisa Sauermann, Dmitrii Zakharov

Suppose we are given matchings $M_{1}, ...., M_{N}$ of size $t$ in some $r$ -uniform hypergraph, and let us think of each matching having a different color. How large does $N$ need to be…

math.NT2024

On the minimal period of integer tilings

Izabella Åaba, Dmitrii Zakharov

If a finite set $A$ tiles the integers by translations, it also admits a tiling whose period $M$ has the same prime factors as $∣ A ∣$ . We prove that the minimal period of such a til…