On Volume Functions of Special Flow Polytopes Associated to the Root System of Type $A$

  • Takayuki Negishi
  • Yuki Sugiyama
  • Tatsuru Takakura


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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