Quivers, cones and polytopes Original Research Article

Let Q be a quiver without oriented cycles. We consider the polytope of flows Δ(θ) in Q with input θ. 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 Δ(θ) for the various inputs θ. Finally, we present several examples.