D'Adderio–Moci: arithmetic matroids

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Library card.

Michele D'Adderio and Luca Moci, "Arithmetic matroids, Tutte polynomial, and toric arrangements," arXiv:1105.3220 (2011).

Arithmetic matroids enrich a matroid with a multiplicity function obeying five axioms (Section 1.3, p. 4) and package the result in an arithmetic Tutte polynomial; those realized by a list of elements of a finitely generated abelian group (Section 1.4) are called representable. The framework distinguishes rational dependence from integral saturation and torsion, information lost by the ordinary cyclotomic matroid.

Its multiplicities record where a rational circuit fails to have a primitive $\{0,\pm1\}$ representative. The paper does not supply a coloring theorem tailored to quasi-independence, so use it as language and invariant machinery rather than as a claimed bridge.