Parole chiave

• polytope
• secondary fan
• hypersimplex
• matroid

Abstract The secondary fan of a polytope stratifies the regular subdivisions of the polytope and provides a combinatorial framework to understand them. We compute this fan for specific polytopes, namely the hypersimplices (2,7) and (3,6). In this case, there are connections to tropical geometry, matroid theory and finite metric spaces. We also find new families of rays of the secondary fan of general hypersimplices.

This is joint work with Michael Joswig and Lars Kastner.