New inequalities for subspace arrangements

Authors:
Ryan Kinser
Affiliations:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, United States
Venue:
Journal of Combinatorial Theory Series A
Year:
2011

Citing 2
Cited 1

Inequalities for Shannon entropy and Kolmogorov complexity

Journal of Computer and System Sciences - Eleventh annual conference on computational learning theory&slash;Twelfth Annual IEEE conference on computational complexity
On characterization of entropy function via information inequalities

IEEE Transactions on Information Theory

Combinatorial representations

Journal of Combinatorial Theory Series A

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Abstract

For each positive integer n=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.