The Polytope of -Subspaces of a Finite Affine Space
The -subspace polytope is defined as the convex hull of the characteristic vectors of all -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 -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...