Algebraic and Topological Combinatorics

Special Session at the Spring Eastern Section Meeting
of the American Mathematical Society

Courant Institute, New York, NY
April 12-13, 2003



Bruce E. Sagan
(Michigan State University)


Topological properties of active orders for matroid bases


Abstract: 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 homotopic to a shellable complex. This helps explain an observation of Las Vergnas that the Möbius function of these lattices is often zero. No background about matroids or shellability will be assumed.

This is joint work with Rieuwert J. Blok (Michigan State University).

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last updated: February 4, 2003