Results 281 to 290 of about 3,263,826 (343)

On the foundations of incidence geometry

Geometriae Dedicata, 1988
Diagram geometries and chamber systems of various types have been used and investigated intensively in recent years - not only in finite group theory, but in other areas as well. This development has led to a need for some clarification of the variations and generalizations introduced by the many authors, and for a discussion of the different axiomatic
F. Buekenhout, D. Buset
semanticscholar   +3 more sources

On the Incidence Geometry of Grassmann Spaces

Geometriae Dedicata, 1999
The main result is a characterization of the Grassmann space \({\mathbf G}\) of a projective space \(\mathcal P\). By definition, the point set \(P\) of \({\mathbf G}\) is the set of lines of \(\mathcal P\), the line set \(\mathcal L\) of \({\mathbf G}\) consists of all plane line pencils in \(\mathcal P\).
FERRARA DENTICE, Eva, MELONE N.
openaire   +2 more sources

Geometric Hyperplanes of Lie Incidence Geometries

Geometriae Dedicata, 1997
Let \(\Gamma=({\mathcal P},{\mathcal L})\) be a geometry of points and lines. A subspace of \(\Gamma\) is a set of points which contains every line that meets it in at least two points. An embedding \(\mu\) of \(\Gamma\) in a finite-dimensional vector space \(V\) consists of a map \(\mu_1\) of \({\mathcal P}\) into the set of 1-subspaces of \(V\) and a
Cooperstein, Bruce N., Shult, Ernest E.
openaire   +2 more sources

Incidence and Metric Geometry

1981
In this section we shall define the notions of an abstract geometry and an incidence geometry. These are given by listing a set of axioms that must be satisfied. After the definitions are made, we will give a number of examples which will serve as models for these geometries.
Richard S. Millman, George D. Parker
openaire   +1 more source

Modal logics for incidence geometries

Journal of Logic and Computation, 1997
Let \(S=(P,L,\text{in})\) be an incidence plane by the well-known axioms: \(P,L\neq\emptyset\); \(\text{in}\subseteq P\times L\); \(P\cap L=\emptyset\); two points are together incident with one and only one line; each line contains at least two different points; each point belongs at least to two different lines.
Balbiani, Philippe   +3 more
openaire   +2 more sources

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