7 papers · 1 filter
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…
Complexes of C-Unbalanced Subsets and Balanced-Subset Posets
Mikhail V. Bludov
Let \(V=\{v_1,\dots,v_m\}\subset\mathbb{R}^d\). We study simplicial complexes arising from subsets of \(V\) whose convex hulls avoid a prescribed convex set. Given a convex set \(C…
Enumerating Minimal Balanced Collections
Mikhail V. Bludov, Nikolai K. Zuev
In this note, we explore the combinatorics of balanced collections. A collection of subsets of the set is called \emph{balanced} if the relative interior of…
On Scarf's theorem for Generalized Cooperative Games
Mikhail V. Bludov, Oleg R. Musin
In this paper, we study a generalization of cooperative games with non-transferable utility. In our model, coalitions are replaced by firms: each firm is assigned a resource vector…
Balanced sets and homotopy invariants of covers
Mikhail V. Bludov
In this paper, we study a construction of homotopy invariants of open or closed covers, where the homotopy class is defined relative to a pair , with a finite set of poi…
Balanced 2-subsets
Mikhail V. Bludov, Oleg R. Musin
Balanced sets appeared in the 1960s in cooperative game theory as a part of nonempty core conditions. In this paper we present a classification of balanced families containing only…
A colored Tverberg type theorem for unavoidable complexes
Mikhail Bludov
The main result of this paper is a "colored Tverberg theorem for rainbow-unavoidable complexes". This theorem may be considered as a merging of two theorems: "Tverberg theorem for…