The isometries of the cut, metric and hypermetric cones

• المؤلفون الرئيسيون: Deza, Antoine., Goldengorin, Boris., Pasechnik, Dmitrii V.
• مؤلفون آخرون: School of Physical and Mathematical Sciences
• التنسيق: مقال
• اللغة: English
• منشور في: 2011
• الموضوعات: DRNTU::Science::Mathematics::Geometry
• الوصول للمادة أونلاين: https://hdl.handle.net/10356/92362; http://hdl.handle.net/10220/6867
• المؤسسة: Nanyang Technological University

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.