Dmitrii Zakharov

activity

20242026

collaborators

4 papers

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…

math.CO2025

Color avoidance for monotone paths

Eion Mulrenin, Cosmin Pohoata, Dmitrii Zakharov

In 2014, Moshkovitz and Shapira determined the tower height for hypergraph Ramsey numbers of tight monotone paths. We address the color-avoiding version of this problem in which on…

math.CO2025

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 $I^´$ -tubes such that $T_{j}$ passes through $p_{j}$ . We prove a lower bound for the numb…

math.CO2024

Generalized Arithmetic Kakeya

Cosmin Pohoata, Dmitrii Zakharov

Around the early 2000-s, Bourgain, Katz and Tao introduced an arithmetic approach to study Kakeya-type problems. They showed that the Euclidean Kakeya conjecture follows from a nat…