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Matroid Automorphisms and Symmetry Groups

Published online by Cambridge University Press:  01 March 2000

LORI FERN
Affiliation:
Mathematics Department, SUNY at Binghamton, Binghamton, NY 13902, USA (e-mail: fern@math.binghamton.edu)
GARY GORDON
Affiliation:
Mathematics Department, Lafayette College, Easton, PA 18042, USA (e-mail: gordong@lafayette.edu)
JASON LEASURE
Affiliation:
Mathematics Department, University of Texas, Austin, TX 78712, USA (e-mail: jleasure@math.utexas.edu)
SHARON PRONCHIK
Affiliation:
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 ≅ = 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.

Type
Research Article
Copyright
2000 Cambridge University Press

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