4 papers
Spanning \(k\)-trees and the colorful Carathéodory theorem
Mikhail Bludov, Alexander Polyanskii
Very recently, using Meshulam's lemma, Blagojević proved a constrained version of the colorful Carathéodory theorem for joins of bipartite spanning trees and wedge of spheres. Our…
Optimal partial plank coverings
Egor Bakaev, Alexander Polyanskii
A plank of width in a Euclidean space is the set of points lying between two parallel hyperplanes at distance from each other. Bang's theorem says that if a family of plank…
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…