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Lattice of integer flows and poset of strongly connected orientations

Combinatorics 2021-01-01 v2

Abstract

We show that the Voronoi cells of the lattice of integer flows of a finite connected graph GG 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 GG. 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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Cite

@article{arxiv.1007.2456,
  title  = {Lattice of integer flows and poset of strongly connected orientations},
  author = {Omid Amini},
  journal= {arXiv preprint arXiv:1007.2456},
  year   = {2021}
}

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12 pages