TY - JOUR

T1 - Finite Homogeneous Metric Spaces

AU - Berestovskii, V. N.

AU - Nikonorov, Yu G.

PY - 2019/9/1

Y1 - 2019/9/1

N2 - 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.

AB - 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.

KW - (semi)regular polytope

KW - finite (normal) homogeneous metric space

KW - finite Clifford-Wolf homogeneous metric space

KW - Kneser graph

KW - vertex-transitive graph

UR - http://www.scopus.com/inward/record.url?scp=85073219250&partnerID=8YFLogxK

U2 - 10.1134/S0037446619050021

DO - 10.1134/S0037446619050021

M3 - Article

AN - SCOPUS:85073219250

VL - 60

SP - 757

EP - 773

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 5

ER -