Conditional Independences among Four Random Variables 2

The conditional independences within a system of four discrete random variables are studied simultaneously. The problem where independences can occur at the same time, called the problem of probabilistic representability, is attacked by an analysis of cones of polymatroids. New results on the cone of all polymatroids satisfying Ingleton inequalities imply a substantial reduction of the problem and an explicit description of the remaining open cases. 3