Flow polytopes with Catalan volumes

@article{Corteel2016FlowPW,
  title={Flow polytopes with Catalan volumes},
  author={Sylvie Corteel and Jang Soo Kim and Karola M'esz'aros},
  journal={Comptes Rendus Mathematique},
  year={2016},
  volume={355},
  pages={248-259}
}
Abstract The Chan–Robbins–Yuen polytope can be thought of as the flow polytope of the complete graph with netflow vector ( 1 , 0 , … , 0 , − 1 ) . The normalized volume of the Chan–Robbins–Yuen polytope equals the product of consecutive Catalan numbers, yet there is no combinatorial proof of this fact. We consider a natural generalization of this polytope, namely, the flow polytope of the complete graph with netflow vector ( 1 , 1 , 0 , … , 0 , − 2 ) . We show that the volume of this polytope… Expand

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