Finite Homogeneous Metric Spaces

Сибирский математический журнал

article

V. N. Berestovskii¹  Yu. G. Nikonorov³ 

[1] Sobolev Institute of Mathematics;Novosibirsk State University;Southern Mathematical Institute, Vladikavkaz Scientific Center of the Russian Academy of Sciences

关键词: finite Clifford–Wolf homogeneous metric space;    finite (normal) homogeneous metric space;    Kneser graph;    (semi)regular polytope;    vertex-transitive graph;   

DOI  :  10.1134/S0037446619050021

学科分类：数学（综合）

来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk

【 摘 要 】

The authors study the class of finite homogeneous metric spaces and some of its important subclasses that have natural definitions in terms of the metrics and well-studied analogs in the class of Riemannian manifolds. The relationships between these classes are explored. The examples of the corresponding spaces are built, some of which are the vertex sets of the special convex polytopes in Euclidean space. We describe the classes on using the language of graph theory, which enables us to provide some examples of finite metric spaces with unusual properties. Several unsolved problems are posed.

【 授权许可】

CC BY