Lattice of Integer Flows and the Poset of Strongly Connected Orientations for Regular Matroids

Autor:	Dancso, Zsuzsanna, Lim, Jongmin
Rok vydání:	2022
Předmět:	Mathematics - Combinatorics 05C21 05C50
Druh dokumentu:	Working Paper
Popis:	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. Comment: 15 pages, minor edits to improve clarity, two references added
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2202.13265 Zobrazit plný text záznamu View this record from Arxiv