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arXiv · 2605.27007

Locally anti-blocking $\mathbf{g}$-polytopes for flow polytopes

Jonah Berggren·Benjamin Braun·Alvaro Cornejo·James Ford McElroy·Chloe' Napier·Zachery Peterson·Williem Rizer·Khrystyna Serhiyenko·Martha Yip
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Abstract

Given an acyclic directed graph (DAG), the space of strength one flows is a lattice polytope called the flow polytope of the DAG. If the DAG admits an ample framing, then the flow polytope is Gorenstein and it linearly projects onto a reflexive polytope called the $\mathbf{g}$-polytope. We provide a combinatorial characterization of amply framed DAGs that have a locally anti-blocking $\mathbf{g}$-polytope, and we characterize the minimal faces of the $\mathbf{g}$-polytope containing a fixed pair of vertices. We prove in this case that the unimodular triangulation of the $\mathbf{g}$-polytope induced by the DKK triangulation of the flow polytope is a pulling triangulation, and we characterize the pulling orders that yield the DKK triangulation. To prove our results, we introduce and study coherence diagrams, a combinatorial model of coherence for amply framed DAGs with locally anti-blocking $\mathbf{g}$-polytopes. We conclude by indicating possible extensions of these results to the setting of $\mathbf{g}$-polytopes for gentle Nakayama algebras.

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Jonah Berggren, Benjamin Braun, Alvaro Cornejo, James Ford McElroy, Chloe' Napier, Zachery Peterson, Williem Rizer, Khrystyna Serhiyenko, Martha Yip. 2026-05-26. Locally anti-blocking $\mathbf{g}$-polytopes for flow polytopes. https://arxiv.org/abs/2605.27007

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