Fans of Tropical Linear Spaces

From CRCG-Wiki

The tropical Grassmannian parameterizes all tropicalizations of ordinary linear spaces and is equiped with a natural fan structure arising from the Gröbner fan. The Grassmannian is contained in the Dressian, which parameterizes tropical linear spaces. The Dressian is also equiped with a Gröbner fan structure, but there is also a natural secondary fan structure arising from the description of the Dressian as the space of matroid subdivisions. We will examine these three fan structures and use the theory of (coarsest) polyhedral subdivisions to give explicit rays of these fans.