Geodesic
On volume functions of special flow polytopes associated to the root system of type \(A\)
The electronic journal of combinatorics, Tome 27 (2020) no. 4
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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 $A$.
DOI : 10.37236/9062
Classification : 52B12, 05A16, 51M25
Mots-clés : flow polytope, volume, root system of type \(A\)

Takayuki Negishi    ; Yuki Sugiyama  1   ; Tatsuru Takakura  1

1 Chuo University 
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     author = {Takayuki Negishi and Yuki Sugiyama and Tatsuru Takakura},
     title = {On volume functions of special flow polytopes associated to the root system of type {\(A\)}},
     journal = {The electronic journal of combinatorics},
     year = {2020},
     volume = {27},
     number = {4},
     doi = {10.37236/9062},
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     url = {http://geodesic.mathdoc.fr/articles/10.37236/9062/}
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Takayuki Negishi; Yuki Sugiyama; Tatsuru Takakura. On volume functions of special flow polytopes associated to the root system of type \(A\). The electronic journal of combinatorics, Tome 27 (2020) no. 4. doi: 10.37236/9062

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