Representations of torsion-free arithmetic matroids
Combinatorics
2023-03-08 v1
Abstract
We study the representability problem for torsion-free arithmetic matroids. By using a new operation called "reduction" and a "signed Hermite normal form", we provide and implement an algorithm to compute all the representations, up to equivalence. As an application, we disprove two conjectures about the poset of layers and the independence poset of a toric arrangement.
Cite
@article{arxiv.1908.04137,
title = {Representations of torsion-free arithmetic matroids},
author = {Roberto Pagaria and Giovanni Paolini},
journal= {arXiv preprint arXiv:1908.04137},
year = {2023}
}