Dmitrii Zakharov

collaborators

3 papers

math.CO2025

Sharp bound for the ErdÅs-Straus non-averaging set problem

Huy Tuan Pham, Dmitrii Zakharov

A set of integers $A$ is non-averaging if there is no element $a$ in $A$ which can be written as an average of a subset of $A$ not containing $a$ . We show that the largest non-aver…

math.MG2025

Spherical sets avoiding orthonormal bases

Dmitrii Zakharov

We show that there exists an absolute constant $c_{0} < 1$ such that for all $n \geq 2$ , any measurable set $A \subset S^{n - 1}$ of density at least $c_{0}$ contains $n$ pairwise orthogona…

math.CO2024

An explicit economical additive basis

Vishesh Jain, Huy Tuan Pham, Mehtaab Sawhney +1

We present an explicit subset $A \subseteq N = {0, 1, \dots}$ such that $A + A = N$ and for all $ε > 0$ , \[\lim_{N\to \infty}\frac{\big|\big\{(n_1,n_2):…

Sharp bound for the ErdÅs-Straus non-averaging set problem

Spherical sets avoiding orthonormal bases

An explicit economical additive basis

Sharp bound for the ErdÅs-Straus non-averaging set problem