%0 Journal Article
%T New inequalities for subspace arrangements
%A Ryan Kinser
%J Mathematics
%D 2009
%I arXiv
%R 10.1016/j.jcta.2009.10.014
%X For each positive integer $n \geq 4$, we give an inequality satisfied by rank functions of arrangements of $n$ subspaces. When $n=4$ we recover Ingleton's inequality; for higher $n$ the inequalities are all new. These inequalities can be thought of as a hierarchy of necessary conditions for a (poly)matroid to be realizable. Some related open questions about the "cone of realizable polymatroids" are also presented.
%U http://arxiv.org/abs/0905.1519v3