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...
Saved in:
| Main Authors: | , , |
|---|---|
| 其他作者: | |
| 格式: | Article |
| 語言: | English |
| 出版: |
2011
|
| 主題: | |
| 在線閱讀: | https://hdl.handle.net/10356/92362 http://hdl.handle.net/10220/6867 |
| 標簽: |
添加標簽
沒有標簽, 成為第一個標記此記錄!
|
| 機構: | Nanyang Technological University |
| 語言: | English |
| 總結: | 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. |
|---|