Finite Homogeneous Metric Spaces

V. N. Berestovskii, Yu G. Nikonorov

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)757-773
Number of pages17
JournalSiberian Mathematical Journal
Volume60
Issue number5
DOIs
Publication statusPublished - 1 Sep 2019

Keywords

  • (semi)regular polytope
  • finite (normal) homogeneous metric space
  • finite Clifford-Wolf homogeneous metric space
  • Kneser graph
  • vertex-transitive graph

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