Locally anti-blocking $\mathbf{g}$-polytopes for flow polytopes
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 -polytope. We provide a combinatorial characterization of amply framed DAGs that have a locally anti-blocking -polytope, and we characterize the minimal faces of the -polytope containing a fixed pair of vertices. We prove in this case that the unimodular triangulation of the -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 -polytopes. We conclude by indicating possible extensions of these results to the setting of -polytopes for gentle Nakayama algebras.
Cite
@article{arxiv.2605.27007,
title = {Locally anti-blocking $\mathbf{g}$-polytopes for flow polytopes},
author = {Jonah Berggren and Benjamin Braun and Alvaro Cornejo and James Ford McElroy and Chloe' Napier and Zachery Peterson and Williem Rizer and Khrystyna Serhiyenko and Martha Yip},
journal= {arXiv preprint arXiv:2605.27007},
year = {2026}
}