Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-09T01:40:24.994Z Has data issue: false hasContentIssue false
  • English
  • Français

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)
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)