On the facets of the secondary polytope |
| |
Authors: | Sven Herrmann |
| |
Institution: | Fachbereich Mathematik, TU Darmstadt, 64289 Darmstadt, Germany |
| |
Abstract: | The secondary polytope of a point configuration A is a polytope whose face poset is isomorphic to the poset of all regular subdivisions of A. While the vertices of the secondary polytope - corresponding to the triangulations of A - are very well studied, there is not much known about the facets of the secondary polytope.The splits of a polytope, subdivisions with exactly two maximal faces, are the simplest examples of such facets and the first that were systematically investigated. The present paper can be seen as a continuation of these studies and as a starting point of an examination of the subdivisions corresponding to the facets of the secondary polytope in general. As a special case, the notion of k-split is introduced as a possibility to classify polytopes in accordance to the complexity of the facets of their secondary polytopes. An application to matroid subdivisions of hypersimplices and tropical geometry is given. |
| |
Keywords: | Polytope Subdivision Triangulation Split Secondary polytope Matroid subdivision Tight span |
本文献已被 ScienceDirect 等数据库收录! |
|