Reconstructing the shape of a tree from observed dissimilarity data
Advances in Applied Mathematics
Duality and minors of secondary polyhedra
Journal of Combinatorial Theory Series B
Subdivisions and triangulations of polytopes
Handbook of discrete and computational geometry
A Geometric Study of the Split Decomposition
Discrete & Computational Geometry
h-Vectors of Gorenstein polytopes
Journal of Combinatorial Theory Series A
SIAM Journal on Discrete Mathematics
Triangulations: Structures for Algorithms and Applications
Triangulations: Structures for Algorithms and Applications
| Hi-index | 0.00 |
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.