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The Polytope of m-Subspaces of a Finite Affine Space

Published online by Cambridge University Press:  21 August 2007

Julie Christophe  and
Jean-Paul Doignon
Julie Christophe
Affiliation:
Université Libre de Bruxelles, c.p. 216, Bd du Triomphe, 1050 Bruxelles, Belgium; doignon@ulb.ac.be
Jean-Paul Doignon
Affiliation:
Université Libre de Bruxelles, c.p. 216, Bd du Triomphe, 1050 Bruxelles, Belgium; doignon@ulb.ac.be
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Abstract

The m-subspace polytope is defined as the convex hull of the characteristic vectors of all m-dimensional subspaces of a finite affine space. The particular case of the hyperplane polytope has been investigated by Maurras (1993) and Anglada and Maurras (2003), who gave a complete characterization of the facets. The general m-subspace polytope that we consider shows a much more involved structure, notably as regards facets. Nevertheless, several families of facets are established here. Then the group of automorphisms of the m-subspace polytope is completely described and the adjacency of vertices is fully characterized.

Keywords

Convex polytopefinite affine spacem-subspace polytope
Type
Research Article
Information
RAIRO - Operations Research , Volume 41 , Issue 3: Journées Polyèdres et Optimisation Combinatoire , July 2007 , pp. 317 - 344
Copyright
© EDP Sciences, ROADEF, SMAI, 2007

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