The University of Michigan Combinatorics Seminar
Las Vergnas recently defined partial orders on the bases
of an ordered matroid using their internal and external activities.
He showed that these posets were in fact graded lattices. We study
the order complex of these lattices, showing that it is always
homotopy equivalent to a shellable complex. This helps explain an
observation of Las Vergnas that the Mobius function of these lattices
is often zero. No background about matroids or shellability will be
assumed. This is joint work with R. Blok.