The polytope of $m$-subspaces of a finite affine space

Christophe, Julie; Doignon, Jean-Paul

doi:10.1051/ro:2007026

Geodesic

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The polytope of

m

-subspaces of a finite affine space

Christophe, Julie ; Doignon, Jean-Paul

RAIRO - Operations Research - Recherche Opérationnelle, Tome 41 (2007) no. 3, pp. 317-344

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Résumé

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.

DOI : 10.1051/ro:2007026

Classification : 51A30, 52B12, 90C27
Keywords: convex polytope, finite affine space, $m$-subspace polytope

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     author = {Christophe, Julie and Doignon, Jean-Paul},
     title = {The polytope of $m$-subspaces of a finite affine space},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {317--344},
     publisher = {EDP-Sciences},
     volume = {41},
     number = {3},
     year = {2007},
     doi = {10.1051/ro:2007026},
     mrnumber = {2348086},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ro:2007026/}
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Christophe, Julie; Doignon, Jean-Paul. The polytope of $m$-subspaces of a finite affine space. RAIRO - Operations Research - Recherche Opérationnelle, Tome 41 (2007) no. 3, pp. 317-344. doi: 10.1051/ro:2007026

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