A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
Finite metrics in switching classes
Tekijät: Ehrenfeucht A, Harju T, Rozenberg G
Kustantaja: ELSEVIER SCIENCE BV
Julkaisuvuosi: 2007
Lehti:: Discrete Applied Mathematics
Tietokannassa oleva lehden nimi: DISCRETE APPLIED MATHEMATICS
Lehden akronyymi: DISCRETE APPL MATH
Vuosikerta: 155
Numero: 1
Aloitussivu: 68
Lopetussivu: 73
Sivujen määrä: 6
ISSN: 0166-218X
DOI: https://doi.org/10.1016/j.dam.2006.04.041
Tiivistelmä
Lt g: D x D -> R be a symmetric function on a finite set D satisfying g(x, x) = 0 for all X E D. A switch g(n) of g w.r.t. a local valuation sigma: D -> R is defined by g(a)(x, y) = sigma(x) + g(x, y) + sigma(y) for x not equal y and g(sigma)(x, x) = 0 for all x. We show that every symmetric function g has a unique minimal semimetric switch, and, moreover, there is a switch of g that is isometric to a finite Manhattan metric. Also, for each metric on D, we associate an extension metric on the set of all nonempty subsets of D, and we show that this extended metric inherits the switching classes on D. (c) 2006 Elsevier B.V. All rights reserved.
Lt g: D x D -> R be a symmetric function on a finite set D satisfying g(x, x) = 0 for all X E D. A switch g(n) of g w.r.t. a local valuation sigma: D -> R is defined by g(a)(x, y) = sigma(x) + g(x, y) + sigma(y) for x not equal y and g(sigma)(x, x) = 0 for all x. We show that every symmetric function g has a unique minimal semimetric switch, and, moreover, there is a switch of g that is isometric to a finite Manhattan metric. Also, for each metric on D, we associate an extension metric on the set of all nonempty subsets of D, and we show that this extended metric inherits the switching classes on D. (c) 2006 Elsevier B.V. All rights reserved.
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