The University of Michigan Combinatorics Seminar
Fall 2003
October 31, 4:10-5:00, 3866 East Hall

Topological properties of active orders for matroid bases

Bruce Sagan

Michigan State University


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.

This talk will be preceded by a pre-talk by Greg Blekherman, from 3:15 to 3:45pm in 3866 East Hall, on notions from matroid theory such as internal and external activity.