Zonotopes whose cellular strings are all coherent
Department
Mathematics
Document Type
Article
Publication Date
8-1-2021
Abstract
A cellular string of a polytope is a sequence of faces stacked on top of each other in a given direction. The poset of cellular strings, ordered by refinement, is known to be homotopy equivalent to a sphere. The subposet of coherent cellular strings is the face lattice of the fiber polytope, hence is homeomorphic to a sphere. In some special cases, every cellular string is coherent. Such polytopes are said to be all-coherent. We give a complete classification of zonotopes with the all-coherence property in terms of their oriented matroid structure. Although the face lattice of the fiber polytope in this case is not an oriented matroid invariant, we prove that the all-coherence property is invariant.
Journal Title
European Journal of Combinatorics
Journal ISSN
01956698
Volume
96
Digital Object Identifier (DOI)
10.1016/j.ejc.2021.103352