Describing the combinatorial structure of the tropical complex C of a
tropical matroid polytope, we obtain a formula for the coarse types of the
maximal cells of C. Due to the connection between tropical complexes and
resolutions of monomial ideals, this yields the generators for the
corresponding coarse type ideal introduced in a recent paper of Dochtermann,
Joswig and Sanyal (2010, preprint arXiv.org:1001.0237). Furthermore, a complete
description of the minimal tropical halfspaces of the uniform tropical matroid
polytopes, i.e. the tropical hypersimplices, is given.Comment: 13 pages, 7 figure