4 papers
Higher-order colossally abundant numbers
Oleg R. Musin
Colossally abundant numbers have large sums of divisors relative to their size. They also admit a geometric description using supporting lines of a planar convex hull. Starting fro…
The Five Distance Theorem For An Arbitrary Norm
Nikita A. Mironov, Oleg R. Musin
The three gap theorem states that the points of the Kronecker sequence , considered modulo one, divide the circle into intervals of at most three distinct lengths.…
Borsuk's conjecture for two-distance sets and its equivalent formulation for graphs
Oleg R. Musin
Every graph G can be embedded in a Euclidean space as a two-distance set. This allows us to reformulate the analogue of Borsuk's conjecture for two-distance sets in terms of graphs…
Positive definite functions in distance geometry
Oleg R. Musin
I. J. Schoenberg proved that a function is positive definite in the unit sphere if and only if this function is a nonnegative linear combination of Gegenbauer polynomials. This fac…