The class of 2-regular matroids is a natural generalisation of regular and near-regular matroids. We prove an excluded-minor characterisation for the class of 2-regular matroids. The class of 3-regular matroids coincides with the class of matroids representable over the Hydra-5 partial field, and the 3-connected matroids in the class with a $U_{2,5}$- or $U_{3,5}$-minor are precisely those with six inequivalent representations over $\mathrm{\text{GF}}(5)$. We also prove that an excluded minor for this class has at most 15 elements.

中文翻译：

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2- 和 3- 正则拟阵的排除未成年人

2-正则拟阵类是正则拟阵和近正则拟阵的自然推广。我们证明了 2-正则拟阵类的排除次要特征。3正则拟阵类与 Hydra-5 部分域上可表示的拟阵类一致，并且该类中的 3 连通拟阵具有$U_{2,5}$- 或者$U_{3,5}$-minor 正是那些具有 6 个不等价表示的那些$\mathrm{\text{GF}}（5）$。我们还证明该类别的排除未成年人最多有 15 个元素。