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Orientable arithmetic matroids
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The theory of matroids has been generalized to oriented matroids and, recently, to arithmetic matroids. We want to give a definition of "oriented arithmetic matroid" and prove some properties like the "uniqueness of orientation".
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Cited by 2 Pith papers
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Representations of torsion-free arithmetic matroids
A new reduction and signed Hermite normal form let every representation of a torsion-free arithmetic matroid be computed up to equivalence, yielding a sharpened upper bound and counterexamples to two shellability conjectures.
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Set of independencies and Tutte polynomial of matroids over a domain
Matroids over a domain admit a Grothendieck-Tutte polynomial with the deletion-contraction property, and the Hilbert series of the associated face module specializes that polynomial.
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