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The Jacobian group (also called the sandpile group, Picard group, or criticalgroup) of a graph or, more generally, of a regular matroid has been wellstudied. Sixth-root-of-unity matroids, also called complex unimodular matroids,are generalizations of regular matroids. This paper provides a definition, andestablishes some basic properties, of the Jacobian group of asixth-root-of-unity matroid.

The Jacobian of a Sixth-Root-of-Unity Matroid