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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
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
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
Linking options:
https://www.mathnet.ru/eng/smj3129 https://www.mathnet.ru/eng/smj/v60/i5/p973
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Abstract page: | 312 | Full-text PDF : | 195 | References: | 38 | First page: | 6 |
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