In this paper we characterize by the facets the convex hull of the characteristic vectors of the hyperplanes of a finite projective space and of a finite affine space.
Dans cet article nous caractérisons, par les facettes, l'enveloppe convexe des vecteurs caractéristiques des hyperplans d'un espace projectif fini et d'un espace affine fini.
@article{RO_2003__37_4_213_0, author = {Anglada, Olivier and Maurras, Jean Fran\c{c}ois}, title = {Enveloppe convexe des hyperplans d'un espace affine fini}, journal = {RAIRO - Operations Research - Recherche Op\'erationnelle}, pages = {213--219}, publisher = {EDP-Sciences}, volume = {37}, number = {4}, year = {2003}, doi = {10.1051/ro:2004007}, zbl = {1096.52001}, language = {fr}, url = {http://archive.numdam.org/articles/10.1051/ro:2004007/} }
TY - JOUR AU - Anglada, Olivier AU - Maurras, Jean François TI - Enveloppe convexe des hyperplans d'un espace affine fini JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2003 SP - 213 EP - 219 VL - 37 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ro:2004007/ DO - 10.1051/ro:2004007 LA - fr ID - RO_2003__37_4_213_0 ER -
%0 Journal Article %A Anglada, Olivier %A Maurras, Jean François %T Enveloppe convexe des hyperplans d'un espace affine fini %J RAIRO - Operations Research - Recherche Opérationnelle %D 2003 %P 213-219 %V 37 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ro:2004007/ %R 10.1051/ro:2004007 %G fr %F RO_2003__37_4_213_0
Anglada, Olivier; Maurras, Jean François. Enveloppe convexe des hyperplans d'un espace affine fini. RAIRO - Operations Research - Recherche Opérationnelle, Volume 37 (2003) no. 4, pp. 213-219. doi : 10.1051/ro:2004007. http://archive.numdam.org/articles/10.1051/ro:2004007/
[1] Upper bounds on the maximal number of facets of -polytopes. Eur. J. Combin. 21 (2000) 121-130. | MR | Zbl
, and ,[2] Some results on the convex hull of the hamiltonian cycles of symetric complete graphs, in Comb. Programming Method Application, Proc. N.A.T.O. advanced institute, edited by B. Roy (1975) 179-180. | MR | Zbl
,[3] An exemple of dual polytopes in the unit hypercube. Ann. Discrete Math. 1 (1977) 391-392. | MR | Zbl
,[4] Convex hull of the edges of a graph and near bipartite graphs. Discrete Math. 46 (1983) 257-265. | MR | Zbl
,[5]
, k-arcs et designs dans les plans projectifs finis. Document interne du GRTC, Marseille (1986).[6] The Line Polytope of a finite Affine Plane. Discrete Math. 115 (1993) 283-286. | MR | Zbl
,[7] Lectures on Modern Geometry. Edizioni Cremonese, Roma (1961). | MR | Zbl
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