Gelfand-Tsetlin Polytopes: A Story of Flow and Order Polytopes

@article{Liu2019GelfandTsetlinPA,
  title={Gelfand-Tsetlin Polytopes: A Story of Flow and Order Polytopes},
  author={Ricky Ini Liu and Karola M'esz'aros and Avery St. Dizier},
  journal={SIAM J. Discret. Math.},
  year={2019},
  volume={33},
  pages={2394-2415}
}
Gelfand-Tsetlin polytopes are prominent objects in algebraic combinatorics. The number of integer points of the Gelfand-Tsetlin polytope $\mathrm{GT}(\lambda)$ is equal to the dimension of the corresponding irreducible representation of $GL(n)$. It is well-known that the Gelfand-Tsetlin polytope is a marked order polytope; the authors have recently shown it to be a flow polytope. In this paper, we draw corollaries from this result and establish a general theory connecting marked order polytopes… 
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