The Nonexistence of Certain Topological Polygons.
The Nonexistence of some Griesmer Arcs in PG(4, 5)
In this paper, we prove the nonexistence of arcs with parameters (232, 48) and (233, 48) in PG(4,5). This rules out the existence of linear codes with parameters [232,5,184] and [233,5,185] over the field with five elements and improves two instances in the recent tables by Maruta, Shinohara and Kikui of optimal codes of dimension 5 over F5.
The n-point-invariants of the projective line and cross-ratios of n-tuples
The nuclei and other properties of -primitive semifield planes.
The number of triangles formed by intersecting diagonals of a regular polygon.
The number of triangles in a tringulation of a set of points in the plane.
The optimal ball and horoball packings to the Coxeter honeycombs in the hyperbolic -space.
The order of a finite Coxeter group.
The Order of Points on the Second Convex Hull of a Simple Polygon.
The orthogonality in affine parallel structure
The partition problem for equifacetal simplices.
The pedal point generation of circular curves of order three in the isotropic plane. (Die Fußpunkterzeugung der zirkulären Kurven 3. Ordnung in der isotropen Ebene.)
The pedal surfaces of -congruences with a one-parameter set of ellipses.
The Planarity of the Equilateral, Isogonal Pentagon.
The Polytope of m-Subspaces of a Finite Affine Space
The m-subspace polytope is defined as the convex hull of the characteristic vectors of all m-dimensional subspaces of a finite affine space. The particular case of the hyperplane polytope has been investigated by Maurras (1993) and Anglada and Maurras (2003), who gave a complete characterization of the facets. The general m-subspace polytope that we consider shows a much more involved structure, notably as regards facets. Nevertheless, several families of facets are established here. Then the...
The Problem of the Circular Billiard.
The projective interpretation of the eight 3-dimensional homogeneous geometries.
The proof of the isomorphism of the -dimensional projective spaces defined axiomatically
The paper gives a proof (without of using of “great” Desargues’ axiom) that any two axiomatically defined n - dimensional projective spaces are isomorphic.
The rank 2 geometries of the simple Suzuki groups .
The Recent Generalizations of Colored Symmetry