The isometries of the cut, metric and hypermetric cones
Metric Geometry
2007-05-23 v1 Group Theory
Abstract
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.
Cite
@article{arxiv.math/0306049,
title = {The isometries of the cut, metric and hypermetric cones},
author = {Antoine Deza and Boris Goldengorin and Dmitrii V. Pasechnik},
journal= {arXiv preprint arXiv:math/0306049},
year = {2007}
}
Comments
8 pages, LaTeX, 2 postscript figures