Representations of torsion-free arithmetic matroids

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.

References in corpus (5)

• Orientable arithmetic matroids
• Two Examples of Toric Arrangements
• Combinatorics of Toric Arrangements
• Shellability of generalized Dowling posets
• Computing the poset of layers of a toric arrangement

Cited by in corpus (1)

• Stanley-Reisner rings for symmetric simplicial complexes, G-semimatroids and Abelian arrangements