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arXiv · 1007.2456

Lattice of integer flows and poset of strongly connected orientations

Omid Amini
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Abstract

We show that the Voronoi cells of the lattice of integer flows of a finite connected graph $G$ in the quadratic vector space of real valued flows have the following very precise combinatorics: the face poset of a Voronoi cell is isomorphic to the poset of strongly connected orientations of subgraphs of $G$. This confirms a conjecture of Caporaso and Viviani {Torelli Theorem For Graphs and Tropical Curves, Duke Math. J. 153(1) (2010), 129-171}.

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Omid Amini. 2020-12-31. Lattice of integer flows and poset of strongly connected orientations. https://arxiv.org/abs/1007.2456

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