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Quivers, cones and polytopes. (English) Zbl 1034.52011
Summary: Let \(Q\) be a quiver without oriented cycles. We consider the polytope of flows \(\Delta(\theta)\) in \(Q\) with input \(\theta\). These polytopes are closely related to the combinatorial structure of the quiver, in particular, to its spanning subtrees. Furthermore, we consider a system of cones which turns out to be a fan and can be seen as a base for the family of all flow polytopes \(\Delta(\theta)\) for the various inputs \(\theta\). Finally, we present several examples.

MSC:
52B05 Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.)
14M25 Toric varieties, Newton polyhedra, Okounkov bodies
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