Volumes of Flow Polytopes Related to Caracol Graphs

Jihyeug Jang, Jang Soo Kim
2020 Electronic Journal of Combinatorics  
Recently, Benedetti et al. introduced an Ehrhart-like polynomial associated to a graph. This polynomial is defined as the volume of a certain flow polytope related to a graph and has the property that the leading coefficient is the volume of the flow polytope of the original graph with net flow vector $(1,1,\dots,1)$. Benedetti et al. conjectured a formula for the Ehrhart-like polynomial of what they call a caracol graph. In this paper their conjecture is proved using constant term identities,
more » ... t term identities, labeled Dyck paths, and a cyclic lemma.
doi:10.37236/9187 fatcat:eyurdpzhsjb7femmv5ptq4lexq