Geodesic
The polytope of m-subspaces of a finite affine space
RAIRO - Operations Research - Recherche Opérationnelle, Tome 41 (2007) no. 3, pp. 317-344

Voir la notice de l'article provenant de la source Numdam

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 
@article{RO_2007__41_3_317_0,
     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/}
}
TY  - JOUR
AU  - Christophe, Julie
AU  - Doignon, Jean-Paul
TI  - The polytope of $m$-subspaces of a finite affine space
JO  - RAIRO - Operations Research - Recherche Opérationnelle
PY  - 2007
SP  - 317
EP  - 344
VL  - 41
IS  - 3
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/ro:2007026/
DO  - 10.1051/ro:2007026
LA  - en
ID  - RO_2007__41_3_317_0
ER  - 
%0 Journal Article
%A Christophe, Julie
%A Doignon, Jean-Paul
%T The polytope of $m$-subspaces of a finite affine space
%J RAIRO - Operations Research - Recherche Opérationnelle
%D 2007
%P 317-344
%V 41
%N 3
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/ro:2007026/
%R 10.1051/ro:2007026
%G en
%F RO_2007__41_3_317_0
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

Cité par Sources :