New inequalities for subspace arrangements

نویسنده

  • Ryan Kinser
چکیده

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.

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عنوان ژورنال:
  • J. Comb. Theory, Ser. A

دوره 118  شماره 

صفحات  -

تاریخ انتشار 2011