D. Zakharov

activity

20182021

collaborators

7 papers

cs.IT2021

On the trifference problem for linear codes

Cosmin Pohoata, Dmitriy Zakharov

We prove that perfect $3$ -hash linear codes in $F_{3}^{n}$ must have dimension at most $(\frac{1}{4} - ε) n$ for some absolute constant $ε > 0$ .

math.CO2021

Norm hypergraphs

Cosmin Pohoata, Dmitriy Zakharov

We introduce a high uniformity generalization of the so-called (projective) norm graphs of Alon, Kollár, Rónyai, and Szabó, and use it to show that $$\operatorname{ex}_{d}(n,K_{s_{…

math.CO2020

Random multilinear maps and the Erdős box problem

David Conlon, Cosmin Pohoata, Dmitriy Zakharov

By using random multilinear maps, we provide new lower bounds for the Erdős box problem, the problem of estimating the extremal number of the complete $d$ -partite $d$ -uniform hyper…

math.CO2020

The extremal number of surfaces

Andrey Kupavskii, Alexandr Polyanskii, István Tomon +1

In 1973, Brown, Erdős and Sós proved that if $H$ is a 3-uniform hypergraph on $n$ vertices which contains no triangulation of the sphere, then $H$ has at most $…

math.CO2020

Turán-type results for intersection graphs of boxes

István Tomon, Dmitriy Zakharov

In this short note, we prove the following analog of the Kővári-Sós-Turán theorem for intersection graphs of boxes. If $G$ is the intersection graph of $n$ axis-parallel boxes in $…

math.MG2019

The right acute angles problem?

Andrey Kupavskii, Dmitriy Zakharov

The Danzer--Grünbaum acute angles problem asks for the largest size of a set of points in $R^{d}$ that determines only acute angles. Recently, the problem was essentially s…