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On volume functions of special flow polytopes
Takayuki Negishi, Yuki Sugiyama, Tatsuru Takakura · 2019-04-10 · via math.CO updates on arXiv.org

In this paper, we consider the volume of a special kind of flow polytope. We show that its volume satisfies a certain system of differential equations, and conversely, the solution of the system of differential equations is unique up to a constant multiple. In addition, we give an inductive formula for the volume with respect to the rank of the root system of type A.

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