TY  - JOUR
AB  - 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)].
AU  - Herrmann, Sven
AU  - Joswig, Michael
DA  - 2008
LA  - eng
IS  - Münster Journal of Mathematics
M2  - 109
PY  - 2008
SP  - 109-142
T2  - Münster Journal of Mathematics
TI  - Splitting polytopes
UR  - https://nbn-resolving.org/urn:nbn:de:hbz:6-43529463487
Y2  - 2024-11-22T12:18:55
ER  -