  Linear information and rank inequalities as, for instance, Ingleton
inequality, are useful tools in information theory and matroid theory. Even
though many such inequalities have been found, it seems that most of them
remain undiscovered. Improved results have been obtained in recent works by
using the properties from which they are derived instead of the inequalities
themselves. We apply here this strategy to the classification of matroids
according to their representations and to the search for bounds on secret
sharing for matroid ports.
