We study the finite projective planes with linear programming models. We give a complete description of the convex hull of the finite projective planes of order . We give some integer linear programming models whose solution are, either a finite projective (or affine) plane of order , or a -arc.
Mots-clés : convex hull, finite projective plane
@article{RO_2008__42_3_285_0, author = {Maurras, Jean-Fran\c{c}ois and Nedev, Roumen}, title = {On the convex hull of projective planes}, journal = {RAIRO - Operations Research - Recherche Op\'erationnelle}, pages = {285--289}, publisher = {EDP-Sciences}, volume = {42}, number = {3}, year = {2008}, doi = {10.1051/ro:2008023}, mrnumber = {2444487}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/ro:2008023/} }
TY - JOUR AU - Maurras, Jean-François AU - Nedev, Roumen TI - On the convex hull of projective planes JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2008 SP - 285 EP - 289 VL - 42 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ro:2008023/ DO - 10.1051/ro:2008023 LA - en ID - RO_2008__42_3_285_0 ER -
%0 Journal Article %A Maurras, Jean-François %A Nedev, Roumen %T On the convex hull of projective planes %J RAIRO - Operations Research - Recherche Opérationnelle %D 2008 %P 285-289 %V 42 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ro:2008023/ %R 10.1051/ro:2008023 %G en %F RO_2008__42_3_285_0
Maurras, Jean-François; Nedev, Roumen. On the convex hull of projective planes. RAIRO - Operations Research - Recherche Opérationnelle, Tome 42 (2008) no. 3, pp. 285-289. doi : 10.1051/ro:2008023. http://archive.numdam.org/articles/10.1051/ro:2008023/
[1] Enveloppe convexe des hyperplans d'un espace affine fini, avec Olivier Anglada. RAIRO-Oper. Res. 37 (2003) 213-219. | Numdam | MR | Zbl
and ,[2]
, http://cgm.cs.mcgill.ca/ avis/C/lrs.html.[3] A pivoting algorithm for convex hulls and vertex enumeration of arrankements and polyhedra. Discrete Comput. Geom. 8 (1992) 295-313. | MR | Zbl
and , and Pór, 0-1 polytopes with many facets, Adv. Math. 161 (2001) 209-228. |[5] The nonexistence of certain finite projective planes. Can. J. Math. 1 (1949) 88-93. | MR | Zbl
and ,[6] Symmetric Hadamard matrices of order 36. Report 70-WSK-02, TH Eindhoven, July (1970). | MR | Zbl
and ,[7]
, www.zib.de/Optimization/Software/porta.[8]
, http://cs.mcgill.ca/ fukuda/soft/cdd.[9] Computing Techniques for the Construction and Analysis of Block Designs1976).
,[10] On a problem in combinations. Camb. Dublin Math. J. 2 (1847) 191-204.
,[11] The Search for a Finite Projective Plane of Order 10. Am. Math. Mon. 98 (1991) 305-318. | MR | Zbl
,[12] Projective embeddings of small Steiner triple systems. Ann. Discrete Math. 7 (1980) 151-173. | MR | Zbl
,[13] Small Steiner triple systems and their properties. Ars Combinatoria 15 (1983) 3-110. | MR | Zbl
, and ,[14] An exemple of dual polytopes in the unit hypercube. Ann. Discrete Math. 1 (1977) 391-392. | MR | Zbl
,[15] The Line Polytope of a finite Affine Plane. Discrete Math. 115 (1993) 283-286. | MR | Zbl
,[16] The double description method, in H.W. Kuhn and A.W. Tucker, Eds., Contributions to theory of games, Vol. 2, Princeton University Press, Princeton (1953). | MR | Zbl
, , and ,[17] Complete classification of the triad systems on fifteen elements. Mem. Nat. Acad. Sci. U.S.A. 14, 2nd memoir (1919) 1-89.
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