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On the Reenements of a Polyhedral Subdivision
| Content Provider | Semantic Scholar |
|---|---|
| Author | Santos, Francisco |
| Copyright Year | 2000 |
| Abstract | Let : P ! Q be an aane projection map between two polytopes P and Q. Billera and Sturmfels introduced in 1992 the concept of polyhedral subdivisions of Q induced by (or-induced) and the ber polytope of the projection: a polytope (P;) of dimension dim(P) ? dim(Q) whose faces are in correspondence with the coherent-induced subdivisions (or-coherent subdivisions). In this paper we investigate the structure of the poset of-induced reenements of a-induced subdivision. In particular, we deene the re-nement polytope associated to any-induced subdivision S, which is a generalization of the ber polytope and shares most of its properties. As applications of the theory we prove that if a point connguration has non-regular subdivisions then it has non-regular triangulations and we provide simple proofs of the existence of non-regular subdivisions for many particular point conngurations. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://matsun1.matesco.unican.es/~santos/Articulos/refine_2000.ps.gz |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
