On the convex hull of projective planes
Jean-François Maurras; Roumen Nedev
RAIRO - Operations Research (2008)
- Volume: 42, Issue: 3, page 285-289
- ISSN: 0399-0559
Access Full Article
topAbstract
topHow to cite
topMaurras, Jean-François, and Nedev, Roumen. "On the convex hull of projective planes." RAIRO - Operations Research 42.3 (2008): 285-289. <http://eudml.org/doc/250408>.
@article{Maurras2008,
abstract = {
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 2. We give some integer linear
programming models whose solution are, either a finite
projective (or affine) plane of order n, or a (n+2)-arc.
},
author = {Maurras, Jean-François, Nedev, Roumen},
journal = {RAIRO - Operations Research},
keywords = {Convex hull; finite projective plane.; convex hull; finite projective plane},
language = {eng},
month = {8},
number = {3},
pages = {285-289},
publisher = {EDP Sciences},
title = {On the convex hull of projective planes},
url = {http://eudml.org/doc/250408},
volume = {42},
year = {2008},
}
TY - JOUR
AU - Maurras, Jean-François
AU - Nedev, Roumen
TI - On the convex hull of projective planes
JO - RAIRO - Operations Research
DA - 2008/8//
PB - EDP Sciences
VL - 42
IS - 3
SP - 285
EP - 289
AB -
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 2. We give some integer linear
programming models whose solution are, either a finite
projective (or affine) plane of order n, or a (n+2)-arc.
LA - eng
KW - Convex hull; finite projective plane.; convex hull; finite projective plane
UR - http://eudml.org/doc/250408
ER -
References
top- O. Anglada and J.F. Maurras, Enveloppe convexe des hyperplans d'un espace affine fini, avec Olivier Anglada. RAIRO-Oper. Res.37 (2003) 213–219.
- D. Avis, avis/C/lrs.html. URIhttp://cgm.cs.mcgill.ca/
- D. Avis and K. Fukuda, A pivoting algorithm for convex hulls and vertex enumeration of arrankements and polyhedra. Discrete Comput. Geom.8 (1992) 295–313.
- I. Bárány and Pór, 0-1 polytopes with many facets, Adv. Math.161 (2001) 209–228.
- R.H. Bruck and H.J. Ryser, The nonexistence of certain finite projective planes. Can. J. Math.1 (1949) 88–93.
- F.C. Bussemaker and J.J. Seidel, Symmetric Hadamard matrices of order 36. Report 70-WSK-02, TH Eindhoven, July (1970).
- T. Christof, www.zib.de/Optimization/Software/porta.
- K. Fukuda, http://cs.mcgill.ca/ fukuda/soft/cdd.
- P.B. Gibbons, Computing Techniques for the Construction and Analysis of Block Designs, Techn. Report N°92, Dept. of Computer Science, University of Toronto (1976).
- T.R. Kirkman, On a problem in combinations. Camb. Dublin Math. J.2 (1847) 191–204.
- C.W.H. Lam, The Search for a Finite Projective Plane of Order 10. Am. Math. Mon.98 (1991) 305–318.
- M. Limbos, Projective embeddings of small Steiner triple systems. Ann. Discrete Math.7 (1980) 151–173.
- R.A Mathon, K.T. Phelps and A. Rosa, Small Steiner triple systems and their properties. Ars Combinatoria15 (1983) 3–110.
- J.F. Maurras, An exemple of dual polytopes in the unit hypercube. Ann. Discrete Math.1 (1977) 391–392.
- J.F. Maurras, The Line Polytope of a finite Affine Plane. Discrete Math.115 (1993) 283–286.
- T.S. Motzkin, H. Raiffa, G.L. Thompson and R.M. Thrall, 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).
- H.S. White, F.N. Cole and L.D. Cummings, Complete classification of the triad systems on fifteen elements. Mem. Nat. Acad. Sci. U.S.A.14, 2nd memoir (1919) 1–89.
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.