Abstract:
Kinser developed a hierarchy of inequalities dealing with the dimensions of certain
spaces constructed from a given quantity of subspaces. These inequalities can
be applied to the rank function of a matroid, a geometric object concerned with
dependencies of subsets of a ground set. A matroid which is representable by a
matrix with entries from some finite field must satisfy each of the Kinser inequalities.
We provide results on the matroids which satisfy each inequality and the
structure of the hierarchy of such matroids.
