Splitting Polytopes
| dc.creator | Herrmann, Sven | |
| dc.creator | Joswig, Michael | |
| dc.date | 2008-05-06 | |
| dc.date | 2008-07-02 | |
| dc.date.accessioned | 2026-07-07T09:47:49Z | |
| dc.date.available | 2026-07-07T09:47:49Z | |
| dc.description | A split of a polytope $P$ is a (regular) subdivision with exactly two maximal cells. It turns out that each weight function on the vertices of $P$ admits a unique decomposition as a linear combination of weight functions corresponding to the splits of $P$ (with a split prime remainder). This generalizes a result of Bandelt and Dress [Adv. Math. 92 (1992)] on the decomposition of finite metric spaces. Introducing the concept of compatibility of splits gives rise to a finite simplicial complex associated with any polytope $P$, the split complex of $P$. Complete descriptions of the split complexes of all hypersimplices are obtained. Moreover, it is shown that these complexes arise as subcomplexes of the tropical (pre-)Grassmannians of Speyer and Sturmfels [Adv. Geom. 4 (2004)]. | |
| dc.description | 25 pages, 7 figures; minor corrections and changes | |
| dc.identifier | https://arxiv.org/abs/0805.0774 | |
| dc.identifier | http://arxiv.org/abs/0805.0774 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/163986 | |
| dc.subject | Combinatorics | |
| dc.subject | Metric Geometry | |
| dc.subject | 52B11; 52B20; 52B30; 52B40; 14M15 | |
| dc.title | Splitting Polytopes | |
| dc.type | text |