convex bodies 1geometric inequalities 1planar convex geometry 1plank covering 1volume maximization 1
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math.CO2026
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…
math.CO2025
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…
math.CO2025
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…