D. Radchenko

collaborators

11 papers

math.MG2026

On GrÃ¼nbaum's problem for symmetric configurations

Andrii Arman, Andriy Bondarenko, Andriy Prymak +1

Let $g_{n}$ be the largest number of Euclidean balls of diameter $1$ which may be needed to cover a set of diameter $1$ in $R^{n}$ . We study this problem for finite sets invar…

math.CO2026

A construction of spherical $5$ -designs with $O (d^{2})$ points

Andrii Arman, Andriy Bondarenko, Andriy Prymak +1

For every $d \geq 1$ we give an explicit equal-weight spherical $5$ -design in $S^{d - 1} \subset R^{d}$ with at most $72 d^{2}$ points. Our approach utilizes recent construc…

math.NT2026

An integrality phenomenon

Florian FÃ¼rnsinn, Danylo Radchenko, Wadim Zudilin

We prove a general statement about the integrality of the sequences generated by a recursion of the following form: $n u_{n}$ equals a linear combination of $u_{n-1},u_{n-2},\dots,u_0…

math.NT2026

Multiple polylogarithms and the Steinberg module

Steven Charlton, Danylo Radchenko, Daniil Rudenko

We establish a connection between multiple polylogarithms on a torus and the Steinberg module of $Q$ , and show that multiple polylogarithms of depth $d$ and weight $n$ can…

math.CA2026

The HÃ¶rmander--Bernhardsson extremal function

Andriy Bondarenko, Joaquim Ortega-CerdÃ, Danylo Radchenko +1

We characterize the function $I ¨ $ of minimal $L^{1}$ norm among all functions $f$ of exponential type at most $I ¨ $ for which $f (0) = 1$ . This function, studied by HÃ¶rmander and Bernha…

math.MG2025

Small Volume Bodies of Constant Width with Tetrahedral Symmetries

Andrii Arman, Andriy Bondarenko, Andriy Prymak +1

For every $n \geq 2$ , we construct a body $U_{n}$ of constant width $2$ in $E^{n}$ with small volume and symmetries of a regular $n$ -simplex. $U_{2}$ is the Reuleaux triangle. To…

On GrÃ¼nbaum's problem for symmetric configurations

A construction of spherical 5-designs with O(d2) points

An integrality phenomenon

Multiple polylogarithms and the Steinberg module

The HÃ¶rmander--Bernhardsson extremal function

Small Volume Bodies of Constant Width with Tetrahedral Symmetries

A construction of spherical $5$ -designs with $O (d^{2})$ points