V. Bilet

activity

20122022

most citedFinite asymptotic clusters of metric spaces

1 citations · 3 across the 8 of their papers we have counts for

collaborators

9 papers

math.CO2022

When all Permutations are Combinatorial Similarities

Viktoriia Bilet, Oleksiy Dovgoshey

Let $(X, d)$ be a semimetric space. A permutation $Φ$ of the set $X$ is a combinatorial self similarity of $(X, d)$ if there is a bijective function $f : d (X^{2}) \to d (X^{2})$ su…

math.MG2021

On equivalence of unbounded metric spaces at infinity

Viktoriia Bilet, Oleksiy Dovgoshey

Let $(X, d)$ be an unbounded metric space. To investigate the asymptotic behavior of $(X, d)$ at infinity, one can consider a sequence of rescaling metric spaces $(X, \frac{1}{r_n}…

math.MG2021

Ultrametrics and complete multipartite graphs

Viktoriia Bilet, Oleksiy Dovgoshey, Yuriy Kononov

We describe the class of graphs for which all metric spaces with diametrical graphs belonging to this class are ultrametric. It is shown that a metric space $(X, d)$ is ultrametric…

math.GN2020

Ultrametric preserving functions and weak similarities of ultrametric spaces

Viktoriia Bilet, Oleksiy Dovgoshey, Ruslan Shanin

Let $W S (X, d)$ be the class of ultrametric spaces which are weakly similar to ultrametric space $(X, d)$ . The main results of the paper completely describe the ultrametric spaces $…

math.MG2018★ 1 cited

Finite asymptotic clusters of metric spaces

Viktoriia Bilet, Oleksiy Dovgoshey

Let $(X, d)$ be an unbounded metric space and let $r ~ = (r_{n})_{n \in N}$ be a sequence of positive real numbers tending to infinity. A pretangent space $Ω_{\infty, \tilde…

math.MG2017★ 1 cited

Asymptotic structure of general metric spaces at infinity

Viktoriia Bilet, Oleksiy Dovgoshey

Let $(X, d)$ be an unbounded metric space and $r ~ = (r_{n})_{n \in N}$ be a scaling sequence of positive real numbers tending to infinity. We define the pretangent space $Ω_…