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Mat. Zametki, 1998, Volume 63, Issue 2, Pages 225–234 (Mi mz1269)  

This article is cited in 1 scientific paper (total in 1 paper)

Decomposition of finite pseudometric spaces

M. É. Mikhailov

Institute of Genetics Academy of Sciences of Moldova

Abstract: Here we define decomposable pseudometrics. A pseudometric is decomposable if it can be represented as the sum of two pseudometrics that are obtained in a way other than the multiplication all distances by a positive factor. We consider spaces consisting of $n$ points. We prove that there exist a finite number of indecomposable pseudometrics (that is, a basis) such that any pseudometric is a linear combination of basic pseudometrics with nonnegative coefficients. For $n\le7$, the basic pseudometrics are listed. A decomposability test is derived for finite pseudometric spaces. We also establish some other conditions of decomposability and indecomposability.

DOI: https://doi.org/10.4213/mzm1269

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English version:
Mathematical Notes, 1998, 63:2, 197–204

Bibliographic databases:

UDC: 515.124
Received: 01.12.1995
Revised: 05.09.1997

Citation: M. É. Mikhailov, “Decomposition of finite pseudometric spaces”, Mat. Zametki, 63:2 (1998), 225–234; Math. Notes, 63:2 (1998), 197–204

Citation in format AMSBIB
\Bibitem{Mik98}
\by M.~\'E.~Mikhailov
\paper Decomposition of finite pseudometric spaces
\jour Mat. Zametki
\yr 1998
\vol 63
\issue 2
\pages 225--234
\mathnet{http://mi.mathnet.ru/mz1269}
\crossref{https://doi.org/10.4213/mzm1269}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1629898}
\zmath{https://zbmath.org/?q=an:0944.54022}
\transl
\jour Math. Notes
\yr 1998
\vol 63
\issue 2
\pages 197--204
\crossref{https://doi.org/10.1007/BF02308759}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000075520700029}


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  • https://doi.org/10.4213/mzm1269
  • http://mi.mathnet.ru/eng/mz/v63/i2/p225

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. É. Mikhailov, “Further criteria for the indecomposability of finite pseudometric spaces”, Math. Notes, 63:3 (1998), 370–373  mathnet  crossref  crossref  mathscinet  zmath  isi
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