Towards the determination of the regular $n$-covers of $PG(3,q)$

Martin Oxenham; Rey Casse

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 $t \geq 1$ ) 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 $2^{ℵ ₀} \leq ℵ ₙ$ .

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 $Ω (\sqrt{n})$ of the triangles determined by the triples.

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

Divisible designs admitting a Suzuki group as an automorphism group

How many clouds cover the plane?

On stabbing triangles by lines in 3-space

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