The isometries of the cut, metric and hypermetric cones |
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| Authors: | Antoine Deza Boris Goldengorin Dmitrii V. Pasechnik |
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| Affiliation: | (1) Dept. of Computing and Software, McMaster University, Hamilton, Ontario, Canada, L8S 4K1;(2) Dept. of Econometrics and Operations Research, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands;(3) Dept. of Applied Mathematics, Khmelnitsky National University, Ukraine;(4) School of Physical and Mathematical Sciences, Nanyang Technological University, 50 Nanyang Avenue, Singapore, 639798 |
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| 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  , that is,  for n ≥ 5. For n = 4 we have  . This result can be extended to cones containing the cuts as extreme rays and for which the triangle inequalities are facet-inducing. For instance,  for n ≥ 5, where Hypn denotes the hypermetric cone. |
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| Keywords: | Polyhedral combinatorics Metric cone Hypermetric cone Symmetry group |
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