Displaying similar documents to “Towards the determination of the regular n -covers of P ⁢ G ⁢ 3 , q ”

2 - ( n 2 , 2 n , 2 n - 1 ) designs obtained from affine planes

Andrea Caggegi (2006)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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The simple incidence structure 𝒟 ( 𝒜 , 2 ) formed by points and unordered pairs of distinct parallel lines of a finite affine plane 𝒜 = ( 𝒫 , ℒ ) of order n > 2 is a 2 - ( n 2 , 2 n , 2 n - 1 ) design. If n = 3 , 𝒟 ( 𝒜 , 2 ) is the complementary design of 𝒜 . If n = 4 , 𝒟 ( 𝒜 , 2 ) is isomorphic to the geometric design A G 3 ( 4 , 2 ) (see [2; Theorem 1.2]). In this paper we give necessary and sufficient conditions for a 2 - ( n 2 , 2 n , 2 n - 1 ) design to be of the form 𝒟 ( 𝒜 , 2 ) for some finite affine plane 𝒜 of order n > 4 . As a consequence we obtain a characterization of small designs 𝒟 ( 𝒜 , 2 ) .

Divisible designs admitting a Suzuki group as an automorphism group

Ralph-Hardo Schulz, Antonino~Giorgio Spera (1998)

Bollettino dell'Unione Matematica Italiana

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Si costruiscono, facendo uso delle rette dei piani di Lüneburg e degli ovali di Tits, due classi di disegni divisibili ipersemplici che ammettono il gruppo di Suzuki S ⁢ q ( q = 2 2 ⁢ t + 1 con t ≥ 1 ) come gruppo di automorfismi. Inoltre si studiano le strutture ottenute determinandone le orbite di S ⁢ q .

How many clouds cover the plane?

James H. Schmerl (2003)

Fundamenta Mathematicae

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The plane can be covered by n + 2 clouds iff 2 ℵ ₀ ≤ ℵ ₙ .

On stabbing triangles by lines in 3-space

Boris Aronov, Jiří Matoušek (1995)

Commentationes Mathematicae Universitatis Carolinae

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We give an example of a set P of 3 n points in ℝ 3 such that, for any partition of P into triples, there exists a line stabbing Ω ( n ) of the triangles determined by the triples.

Finite projective planes, Fermat curves, and Gaussian periods

Koen Thas, Don Zagier (2008)

Journal of the European Mathematical Society

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One of the oldest and most fundamental problems in the theory of finite projective planes is to classify those having a group which acts transitively on the incident point-line pairs (flags). The conjecture is that the only ones are the Desarguesian projective planes (over a finite field). In this paper, we show that non-Desarguesian finite flag-transitive projective planes exist if and only if certain Fermat surfaces have no nontrivial rational points, and formulate several other equivalences...