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Title: The isometries of the cut, metric and hypermetric cones
Authors: Deza, Antoine.
Goldengorin, Boris.
Pasechnik, Dmitrii V.
Keywords: DRNTU::Science::Mathematics::Geometry
Issue Date: 2006
Source: Deza, A., Goldengorin, B., & Pasechnik, D. V. (2006). The isometries of the cut, metric and hypermetric cones. Journal of Algebraic Combinatorics, 23, 197-203.
Series/Report no.: Journal of algebraic combinatorics
Abstract: We show that the symmetry groups of the cut cone Cutn and the metric cone Metn both consist of the isometries induced by the permutations on {1, . . . , n}; that is, Is(Cutn) = Is(Metn) ≃ Sym(n) for n ≥ 5. For n = 4 we have Is(Cut4) = Is(Met4) ≃ Sym(3) × Sym(4). This result can be extended to cones containing the cuts as extreme rays and for which the triangle inequalities are facet-inducing. For instance, Is(Hypn) ≃ Sym(n) for n ≥ 5, where Hypn denotes the hypermetric cone.
Rights: © 2006 Springer Science+Business Media. This is the author created version of a work that has been peer reviewed and accepted for publication by Journal of Algebraic Combinatorics, Springer Science+Business Media. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at the following DOI:
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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