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arXiv · 1911.10703

Volumes of flow polytopes related to caracol graphs

Jihyeug Jang·Jang Soo Kim
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Abstract

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, labeled Dyck paths, and a cyclic lemma.

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Jihyeug Jang, Jang Soo Kim. 2019-11-25. Volumes of flow polytopes related to caracol graphs. https://arxiv.org/abs/1911.10703

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