The isometries of the cut, metric and hypermetric cones
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...
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sg-ntu-dr.10356-923622023-02-28T19:24:20Z The isometries of the cut, metric and hypermetric cones Deza, Antoine. Goldengorin, Boris. Pasechnik, Dmitrii V. School of Physical and Mathematical Sciences DRNTU::Science::Mathematics::Geometry 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. Accepted version 2011-07-06T02:50:13Z 2019-12-06T18:22:00Z 2011-07-06T02:50:13Z 2019-12-06T18:22:00Z 2006 2006 Journal Article Deza, A., Goldengorin, B., & Pasechnik, D. V. (2006). The isometries of the cut, metric and hypermetric cones. Journal of Algebraic Combinatorics, 23, 197-203. https://hdl.handle.net/10356/92362 http://hdl.handle.net/10220/6867 10.1007/s10801-006-6924-6 en Journal of algebraic combinatorics © 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: http://dx.doi.org/10.1007/s10801-006-6924-6. 8 p. application/pdf |
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DRNTU::Science::Mathematics::Geometry Deza, Antoine. Goldengorin, Boris. Pasechnik, Dmitrii V. The isometries of the cut, metric and hypermetric cones |
| description |
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. |
| author2 |
School of Physical and Mathematical Sciences |
| author_facet |
School of Physical and Mathematical Sciences Deza, Antoine. Goldengorin, Boris. Pasechnik, Dmitrii V. |
| format |
Article |
| author |
Deza, Antoine. Goldengorin, Boris. Pasechnik, Dmitrii V. |
| author_sort |
Deza, Antoine. |
| title |
The isometries of the cut, metric and hypermetric cones |
| title_short |
The isometries of the cut, metric and hypermetric cones |
| title_full |
The isometries of the cut, metric and hypermetric cones |
| title_fullStr |
The isometries of the cut, metric and hypermetric cones |
| title_full_unstemmed |
The isometries of the cut, metric and hypermetric cones |
| title_sort |
isometries of the cut, metric and hypermetric cones |
| publishDate |
2011 |
| url |
https://hdl.handle.net/10356/92362 http://hdl.handle.net/10220/6867 |
| _version_ |
1759856785912496128 |