Imbrex geometries

Imbrex geometries

We introduce an axiom on strong parapolar spaces of diameter 2, which arises naturally in the framework of Hjelmslev geometries. This way, we characterize the Hjelmslev-Moufang plane and its relatives (line Grassmannians, certain half-spin geometries and Segre geometries). At the same time we provide a more general framework for a lemma of Cohen, which is widely used to study parapolar spaces. ...

Homogeneous Geometries

For the purposes of this paper, a geometry will consist of a set together with a closure operation on that set, satisfying the exchange condition, and under which singletons are closed (for more precise definitions, see §2.1). The geometry is homogeneous if in the automorphism group of the geometry, the pointwise stabilizer of any finitedimensional closed subset of the geometry is transitive on...

Spacetime Geometries

Injection geometries

In this paper a new concept, injection geometries, is considered. This provides a common generalization of matroids and permutation geometries. Different systems of axioms and various examples are given. Theorem 5.1 provides an extremal set theoretic characterization of injection designs. 0 1984 Academic Press, Inc.

Partial Geometries

The main purpose of this paper is to survey recent results on partial geometries. I t is now twenty years since Bose [1] introduced the concept of a partial geometry in order to study large cliques in strongly regular graphs. Several strong necessary conditions for the existence of strongly regular graphs also have consequences for the existence question for partial geometries. We give the nece...