1 citations · 2 across the 9 of their papers we have counts for
5 papers · 1 filter
Borsuk-Ulam type theorem for the orthogonal group and orthogonal four-partitions
Oleg R. Musin
Makeev [2] stated that every finite Borel measure in assigning zero mass to hyperplanes can be cut by mutually orthogonal hyperplanes so that every pair divides t…
Computing the Hopf invariant
Oleg R. Musin, Timur Shamazov
We consider Whitehead's integral formula and propose an algorithm for computing the Hopf invariant for simplicial mappings.
Algorithms for orthogonal partitioning into four parts
Alexey Fakhrutdinov, Oleg R. Musin
The famous pancake theorem states that for every finite set in the plane, there exist two orthogonal lines that divide into four equal parts. We propose an algorithm whose…
Minimal simplicial spherical mappings with a given degree
Ksenia Apolonskaya, Oleg R. Musin
This paper studies the minimal number of vertices required in a triangulation of the -sphere to admit a simplicial map to the boundary of a -simplex with a given…
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…