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Matroid Automorphisms and Symmetry Groups

Published online by Cambridge University Press:  01 March 2000

LORI FERN ,
GARY GORDON ,
JASON LEASURE  and
SHARON PRONCHIK
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)
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Abstract

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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.

Information

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 9 , Issue 2 , March 2000 , pp. 105 - 123
Copyright
2000 Cambridge University Press