Andrii Arman

collaborators

3 papers

math.MG2026

On Grünbaum'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.MG2025

On asymptotic Lebesgue's universal covering problem

Andrii Arman, Andriy Bondarenko, Andriy Prymak +1

Universal cover in $E^{n}$ is a measurable set that contains a congruent copy of any set of diameter 1. Lebesgue's universal covering problem, posed in 1914, asks for the…

math.MG2025

Illumination number of 3-dimensional cap bodies

Andrii Arman, Jaskaran Singh Kaire, Andriy Prymak

The illumination conjecture asserts that any convex body in $n$ -dimensional Euclidean space can be illuminated by at most $2^{n}$ external light sources or parallel beams of light. D…