Units

Discrete Mathematics

Projetcs

Characterization of the orbit numbers on the i-faces of d-polytopes

A d-polytope P is a convex polytope of the Euclidean space of dimension d. The full automorphism group of P has a certain number of orbits on the points, the edges,..., the i-faces (faces of dimension i),..., and on the (d-1)-faces of P. These numbers determine a d-vector. Characterization of the set of the possible d-vectors, in particular for d=3.

Classification of homogeneous and ultrahomogeneous structures

A structure S is said to be homogeneous (resp.ultrahomogeneous) if when two finite substructures of S are isomorphic, then one of (resp.all of) these isomorphisms can be extended into an automorphism of S. Classification of homogeneous and ultrahomogeneous linear and semilinear spaces, Steiner systems...