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<p>The Jacobian group (also called the sandpile group, Picard group, or critical group) of a graph or, more generally, of a regular matroid has been well studied. Sixth-root-of-unity matroids, also called complex unimodular matroids, are generalizations of regular matroids. This paper provides a definition, and establishes some basic properties, of the Jacobian group of a sixth-root-of-unity matroid.</p>

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

  • 期刊论文

  • 发表日期：

    2026年7月11日

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  • Matthew Baker,
  • Changxin Ding,
  • Xu Zhuang

摘要

The Jacobian group (also called the sandpile group, Picard group, or critical group) of a graph or, more generally, of a regular matroid has been well studied. Sixth-root-of-unity matroids, also called complex unimodular matroids, are generalizations of regular matroids. This paper provides a definition, and establishes some basic properties, of the Jacobian group of a sixth-root-of-unity matroid.