Projective Planes in Irreducible 3-Manifolds.
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G. Ananda Swarup (1973)
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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.
Costantino, F. (2002)
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Roland Coghetto (2017)
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Using the Mizar system [2], we formalized that homographies of the projective real plane (as defined in [5]), form a group. Then, we prove that, using the notations of Borsuk and Szmielew in [3] “Consider in space ℝℙ2 points P1, P2, P3, P4 of which three points are not collinear and points Q1,Q2,Q3,Q4 each three points of which are also not collinear. There exists one homography h of space ℝℙ2 such that h(Pi) = Qi for i = 1, 2, 3, 4.” (Existence Statement 52 and Existence Statement 53)...