Lattice of Integer Flows and the Poset of Strongly Connected Orientations for Regular Matroids
Abstract
A 2010 result of Amini provides a way to extract information about the structure of the graph from the geometry of the Voronoi polytope of the lattice of integer flows (which determines the graph up to two-isomorphism). Specifically, Amini shows that the face poset of the Voronoi polytope is isomorphic to the poset of strongly connected orientations of subgraphs. This answers a question raised by Caporaso and Viviani, and Amini also proves a dual result for integer cuts. In this paper we generalise Amini's result to regular matroids; in this context the theorem for integer cuts becomes a direct consequence of the theorem for integer flows, by making duality explicit as matroid duality.
Keywords
Cite
@article{arxiv.2202.13265,
title = {Lattice of Integer Flows and the Poset of Strongly Connected Orientations for Regular Matroids},
author = {Zsuzsanna Dancso and Jongmin Lim},
journal= {arXiv preprint arXiv:2202.13265},
year = {2023}
}
Comments
15 pages, minor edits to improve clarity, two references added