M. Bludov

collaborators

6 papers

math.CO2026

Spanning $k$-trees and the colorful CarathÃ©odory theorem

Mikhail Bludov, Alexander Polyanskii

Very recently, using Meshulam's lemma, BlagojeviÄ proved a constrained version of the colorful CarathÃ©odory theorem for joins of bipartite spanning trees and wedge of spheres. Ou…

math.CO2025

On the Homotopy Type of Balanced subsets

Mikhail V. Bludov

For a finite set of points $V = {v_{1}, \dots, v_{m}}$ in Euclidean space $R^{d}$ and a point $r \in R^{d}$ , a subset $S \subset V$ is called $r$ -balanced if $\mathrm{rel…

math.AT2025

On essential simplicial maps $S^{3} \to S^{2}$

Mikhail V. Bludov, Sergei Vad. Fomin, Oleg R. Musin

A fiber-uniform bound on the complexity of an essential simplicial map $S^{3} \to S^{2}$ is proven, and the tightness of the bound is investigated. It follows that the triangula…

math.CO2025

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 $[n] = {1, \dots, n}$ is called \emph{balanced} if the relative interior of…

math.CO2025

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…

math.CO2025

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 $(V, r)$ , with $V$ a finite set of poi…

Spanning \(k\)-trees and the colorful CarathÃ©odory theorem

On the Homotopy Type of Balanced subsets

On essential simplicial maps S3→S2

Enumerating Minimal Balanced Collections

On Scarf's theorem for Generalized Cooperative Games

Balanced sets and homotopy invariants of covers

On essential simplicial maps $S^{3} \to S^{2}$