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m-subspace polytope

RAIRO - Operations Research (1)

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The Polytope of m-Subspacesof a Finite Affine Space
Julie Christophe, Jean-Paul Doignon
Journal:

RAIRO - Operations Research / Volume 41 / Issue 3 / July 2007

Published online by Cambridge University Press:

21 August 2007, pp. 317-344

Print publication:

July 2007
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The m-subspace polytope is defined as the convex hull of the characteristic vectors of all m-dimensional subspaces ofa finite affine space. The particular case of the hyperplane polytopehas 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.