From the 1 of 6 linked papers with an AI index.
6 papers
Optimal partial plank coverings
Egor Bakaev, Alexander Polyanskii
The paper investigates how to place planks of a fixed total width to cover the largest possible volume of a convex body, proving that for a Euclidean ball and for any planar convex…
Spanning \(k\)-trees and the colorful Carathéodory theorem
Mikhail Bludov, Alexander Polyanskii
Very recently, using Meshulam's lemma, BlagojeviÄ proved a constrained version of the colorful Carathéodory theorem for joins of bipartite spanning trees and wedge of spheres. Ou…
Triangle covering problems and the Viterbo inequality in the plane
Alexey Balitskiy, Ivan Mitrofanov, Alexander Polyanskii
We review a certain problem on covering triangles in the plane. Equivalently, it can be viewed as a family of 'isobilliard' inequalities in convex shapes, and as a special case of…
Tight colorful no-dimensional Tverberg theorem
Polina Barabanshchikova, Grigory Ivanov, Alexander Polyanskii
We study colorful no-dimensional Tverberg-type problems and obtain several optimal results. A colorful no-dimensional Tverberg-type theorem provides a bound on a radius such th…
New Helly-type results for discrete boxes: Quantitative colorful and -variants
Rahul Gangopadhyay, Alexander Polyanskii, Wei Rao
In 2008, Halman showed that for any finite set and any finite family of axis-parallel boxes in , if the intersection of and a…
No-dimensional Tverberg-type problems
Alexander Polyanskii
Recently, Adiprasito et al. have initiated the study of the so-called no-dimensional Tverberg problem. This problem can be informally stated as follows: Given , partition…