HUYBRECHTS Cécile

## Units

Discrete Mathematics

## Projetcs

Theory of the incidence geometries of type L.Af* satisfying an intersection axiom

Generalizing results on the geometries with diagrams C.Af* and Af.Af*, it is possible to show that under certain hypothesis, every geometry on L.Af* is embeddable in a geometry on L.A2 and to pursue its study on this basis

The permutohedron as a permutograph

The permotuhedron is a graph used both in geometry and in the study of rankings. It is shown to belong to a whole family of graphs, called the permutographs. The automorphisms and the polytopal character of these graphs are investigated.

Arithmetic and grouptheoretical reduction of rank 3 amalgams of thick linear spaces that are flag-homogeneous

The polynomial structure of orders of thick flag-homogeneous linear spaces puts strong constraints on the orders of rank 3 amalgams of such geometries from which a reduced list of diagrams is derived. Under the additional hypothesis where the amalgam is endowed with a chamber-transitive automorphism group the analysis of rank one parabolic subgroups leads to further reductions

Gates of convex sets

The notion of a gate for a subset in a metric space plays a role in localization theory (belonging to operations research) and in the theory of buildings (belonging to geometry). It is investigated in normed vector spaces