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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 $𝒟 (𝒜, 2)$ .

24 self-inscribed decagons in Desargues configuration $10_{3}$

Kishore Sinha (1976)

Časopis pro pěstování matematiky

2-blocking sets in PG(4, $q$ ), $q$ square.

Metsch, Klaus, Storme, L. (2000)

Beiträge zur Algebra und Geometrie

2-frieze patterns and the cluster structure of the space of polygons

Sophie Morier-Genoud, Valentin Ovsienko, Serge Tabachnikov (2012)

Annales de l’institut Fourier

We study 2-frieze patterns generalizing that of the classical Coxeter-Conway frieze patterns. The geometric realization of this space is the space of $n$ -gons (in the projective plane and in 3-dimensional vector space) which is a close relative of the moduli space of genus $0$ curves with $n$ marked points. We show that the space of 2-frieze patterns is a cluster manifold and study its algebraic and arithmetic properties.

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$ℳ$ -Bewegungen mit den $(U)$ -Automorphismen

$*$ -biregular rings

$(n, 2)$ -axonometries and the contour of hyperspheres.

$(S_{3}, S_{6})$ -Amalgams IV

$(S_{3}, S_{6})$ -Amalgams V

$(S_{3}, S_{6})$ -Amalgams VI

$(S_{3}, S_{6})$ -Amalgams VII

100 let „Základů geometrie‟: Rozhodující příspěvek Davida Hilberta k formalizaci matematiky

16-dimensional compact projective planes with 3 fixed points.

1-Dimensional Orbits in Flat Projective Planes.

$2 - (n^{2}, 2 n, 2 n - 1)$ designs obtained from affine planes

24 self-inscribed decagons in Desargues configuration $10_{3}$

2-blocking sets in PG(4, $q$ ), $q$ square.

2-frieze patterns and the cluster structure of the space of polygons

2-manifold surfaces and space partitions

2-transitiv abstract ovals of odd order.

3D illustrations to Chapter 8 of Cromwell's Polyhedra

4-dimensional Minkowski planes with large automorphism group.

4-dimensionale Translationsebenen.

4-dimensionale Translationsebenen mit 7-dimensionaler Kollineationsgruppe.

Currently displaying 1 – 20 of 209