The h-vector of the union of two sets of points in the projective plane

Given two h-vectors, h and h', we study which are the possible h-vectors for the union of two disjoint sets of points in P^2 , respectively associated to h and h' and how they can be constructed. We will give some bounds for the resulting h-vector and we will show how to construct the minimal h-vector of the union among all possible ones

Parallele Algorithmen für rationale Kegel und affine Monoide

This thesis presents parallel algorithms for rational cones and affine monoids which pursue two main computational goals: finding the Hilbert basis, a minimal generating system of the monoid of lattice points of a cone; and counting elements degree-wise in a generating function, the Hilbert series