# Representations of torsion-free arithmetic matroids.

@inproceedings{Pagaria2019RepresentationsOT, title={Representations of torsion-free arithmetic matroids.}, author={Roberto Pagaria and Giovanni Paolini}, year={2019} }

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.

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