EuDML | Browse

The search session has expired. Please query the service again.

Items

All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Page 1 Next

Displaying 1 – 20 of 161

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

Andrea Caggegi (2006)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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 $𝒟 (𝒜, 2)$ .

Currently displaying 1 – 20 of 161

Page 1 Next

Displaying 1 – 20 of 161

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

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

A classification of finite homogeneous semilinear spaces.

A family of complete arcs in finite projective planes

A note on embedding and generating dual polar spaces.

A note on the derived semifield planes of order 16.

A theorem of O'Nan for finite linear spaces

A unified construction of finite geometries associated with $q$ -clans in characteristic 2.

A unified treatment of the theories of matroids with coefficients and of $Δ$ -matroids with coefficients.

Affine Hjelmslev-Ebenen mit verfeinerten Nachbarschaftsrelationen.

Affine Triple Systems and Matroid Designs.

An alternative definition of the notion valuation in the theory of near polygons.

An asymptotic Gilbert-Varshamov bound for $(T, M, S)$ -nets.

An extremal characterization of projective planes.

Another case of the prime power conjecture for finite projective planes.

Arcs with large conical subsets.

Binary multiples of combinatorial geometries

Binary multiples of combinatorial geometries - II

Biplanes.

Blocking sets of 16 points in projective planes of order 10 - III

Currently displaying 1 – 20 of 161