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Title:
Unbounded matroids
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Abstract:
An unbounded matroid on a finite set E is a (possibly) unbounded generalized permutohedron in R^E such that all its vertices have 0-1 coordinates. Associated to each such polyhedron Q is a poset S on E coming from the recession cone of Q. We will explain how the theory of these polyhedra admits several cryptomorphic descriptions that specialize to classical matroid theory if we take S to be an antichain and to polymatroid theory if we allow S to be a disjoint union of chains. We show that each such polyhedron can be constructed (non-uniquely) from a matroid and a poset on E. Then we use this to produce several matroid
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