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 ≅ = Aut(MW). This allows us to connec...

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Bibliographic Details
Published in:Combinatorics, probability & computing probability & computing, 2000-03, Vol.9 (2), p.105-123
Main Authors: FERN, LORI, GORDON, GARY, LEASURE, JASON, PRONCHIK, SHARON
Format: Article
Language:English
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Summary: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.
ISSN:0963-5483
1469-2163
DOI:10.1017/S0963548399004125