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Sibirskii Matematicheskii Zhurnal, 2019, Volume 60, Number 5, Pages 973–995
DOI: https://doi.org/10.33048/smzh.2019.60.502 (Mi smj3129) 		 
This article is cited in 11 scientific papers (total in 11 papers)

Finite homogeneous metric spaces

V. N. Berestovskiiab, Yu. G. Nikonorovc

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
c Southern Mathematical Institute, Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz, Russia
Full-text PDF (518 kB) Citations (11)
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DOI: https://doi.org/10.33048/smzh.2019.60.502
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.
Keywords: finite Clifford–Wolf homogeneous metric space, finite (normal) homogeneous metric space, Kneser graph, (semi)regular polytope, vertex-transitive graph.
Received: 25.12.2018
Revised: 25.12.2018
Accepted: 12.03.2019
English version:
Siberian Mathematical Journal, 2019, Volume 60, Issue 5, Pages 757–773
DOI: https://doi.org/10.1134/S0037446619050021
Bibliographic databases:
Document Type: Article
UDC: 515.124.4+514.172.4+512.542+519.173
Language: Russian
Citation: V. N. Berestovskii, Yu. G. Nikonorov, “Finite homogeneous metric spaces”, Sibirsk. Mat. Zh., 60:5 (2019), 973–995; Siberian Math. J., 60:5 (2019), 757–773
Citation in format AMSBIB
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    • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский математический журнал Siberian Mathematical Journal
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