Matroid Automorphisms and Symmetry Groups
For a subgroup W of the hyperoctahedral group On which is generated by reflections, we consider the linear dependence matroid MW on the column vectors corresponding to the reflections in W. We determine all possible automorphism groups of MW and determine when W [congruent with] = Aut(MW). This allows us to connect combinatorial and geometric symmetry. Applications to zonotopes are also considered. Signed graphs are used as a tool for constructing the automorphisms.(Received February 18 1998)
(Revised November 8 1998)
1 This research was supported by NSF REU grant DMS-9424098.