Combinatorics, Probability and Computing



Matroid Automorphisms and Symmetry Groups


LORI FERN a1, GARY GORDON a2, JASON LEASURE a3 and SHARON PRONCHIK a4 1
a1 Mathematics Department, SUNY at Binghamton, Binghamton, NY 13902, USA (e-mail: fern@math.binghamton.edu)
a2 Mathematics Department, Lafayette College, Easton, PA 18042, USA (e-mail: gordong@lafayette.edu)
a3 Mathematics Department, University of Texas, Austin, TX 78712, USA (e-mail: jleasure@math.utexas.edu)
a4 Mathematics Department, Lafayette College, Easton, PA 18042, USA (e-mail: sharon.pronchik@sdrc.com)

Abstract

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)



Footnotes

1 This research was supported by NSF REU grant DMS-9424098.