18 citations · 18 across the 10 of their papers we have counts for
12 papers · 1 filter
On Grünbaum's problem for symmetric configurations
Andrii Arman, Andriy Bondarenko, Andriy Prymak +1
Let be the largest number of Euclidean balls of diameter which may be needed to cover a set of diameter in . We study this problem for finite sets invar…
Exponential bounds for the spherical Blaschke-Lebesgue problem
Abigail Hall, Andriy Prymak, Chanatip Sujsuntinukul
The Blaschke-Lebesgue theorem states that the Reuleaux triangle has the smallest area among planar convex bodies of a fixed constant width. We study how small bodies of constant wi…
On asymptotic Lebesgue's universal covering problem
Andrii Arman, Andriy Bondarenko, Andriy Prymak +1
Universal cover in 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…
Hadwiger's conjecture for cap bodies
Andrii Arman, Jaskaran Singh Kaire, Andriy Prymak
Hadwiger's covering conjecture states that every -dimensional convex body can be covered by at most of its smaller positive homothetic translates, with copies requir…
Illumination number of 3-dimensional cap bodies
Andrii Arman, Jaskaran Singh Kaire, Andriy Prymak
The illumination conjecture asserts that any convex body in -dimensional Euclidean space can be illuminated by at most external light sources or parallel beams of light. D…
On a Gallai-type problem and illumination of spiky balls and cap bodies
Andrii Arman, Andriy Bondarenko, Andriy Prymak +1
We show that any finite family of pairwise intersecting balls in can be pierced by points improving the previously known estimate of $(2+o(1))^…