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Lawrence Polytopes

Published online by Cambridge University Press:  20 November 2018

Margaret Bayer  and
Bernd Sturmfels
Margaret Bayer
Affiliation:
University of Kansas, Lawrence, Kansas
Bernd Sturmfels
Affiliation:
Johannes - Kepler - Universität Linz, Linz, Austria
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In 1980 Jim Lawrence suggested a construction Λ which assigns to a given rank r oriented matroid M on n points a rank n + r oriented matroid Λ(M) on 2n points such that the face lattice of Λ(M) is polytopal if and only if M is realizable. The Λ-construction generalized a technique used by Perles to construct a nonrational polytope [10]. It was used by Lawrence to prove that the class of polytopal lattices is strictly contained in the class of face lattices of oriented matroids (unpublished) and by Billera and Munson to show that the latter class is not closed under polarity. See [4] for a discussion of this construction and both of these applications.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 42 , Issue 1 , 01 February 1990 , pp. 62 - 79
Copyright
Copyright © Canadian Mathematical Society 1990

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