316 research outputs found
The isometries of the cut, metric and hypermetric cones
We show that the symmetry groups of the cut cone Cut(n) and the metric cone
Met(n) both consist of the isometries induced by the permutations on {1,...,n};
that is, Is(Cut(n))=Is(Met(n))=Sym(n) for n>4. For n=4 we have
Is(Cut(4))=Is(Met(4))=Sym(3)xSym(4).
This is then extended to cones containing the cuts as extreme rays and for
which the triangle inequalities are facet-inducing. For instance,
Is(Hyp(n))=Sym(n) for n>4, where Hyp(n) denotes the hypermetric cone.Comment: 8 pages, LaTeX, 2 postscript figure
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