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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.
Christophe, Julie, and Doignon, Jean-Paul. "The Polytope of m-Subspaces of a Finite Affine Space." RAIRO - Operations Research 41.3 (2007): 317-344. <http://eudml.org/doc/250126>.
@article{Christophe2007, 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.
}, author = {Christophe, Julie, Doignon, Jean-Paul}, journal = {RAIRO - Operations Research}, keywords = {Convex polytope; finite affine space; m-subspace polytope; convex polytope; -subspace polytope}, language = {eng}, month = {8}, number = {3}, pages = {317-344}, publisher = {EDP Sciences}, title = {The Polytope of m-Subspaces of a Finite Affine Space}, url = {http://eudml.org/doc/250126}, volume = {41}, year = {2007}, }
TY - JOUR AU - Christophe, Julie AU - Doignon, Jean-Paul TI - The Polytope of m-Subspaces of a Finite Affine Space JO - RAIRO - Operations Research DA - 2007/8// PB - EDP Sciences VL - 41 IS - 3 SP - 317 EP - 344 AB -
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.
LA - eng KW - Convex polytope; finite affine space; m-subspace polytope; convex polytope; -subspace polytope UR - http://eudml.org/doc/250126 ER -
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