From the configuration of a matroid (which records the size and rank of the cyclic flats and the containments among them, but not the sets), one can compute several much-studied matroid invariants, including the Tutte polynomial and a newer, stronger invariant, the $\mathcal{G}$-invariant. To gauge how much additional information the configuration contains compared to these invariants, it is of interest to have methods for constructing matroids with different configurations but the same $\mathcal{G}$-invariant. We offer several such constructions along with tools for developing more.

中文翻译：

---

具有不同配置和相同 G 不变性的拟阵

从拟阵的配置（它记录循环平面的大小和等级以及它们之间的包含，但不记录集合），可以计算几个经过大量研究的拟阵不变量，包括 Tutte 多项式和一个更新、更强的不变量，这$\mathcal{G}$-不变的。为了衡量与这些不变量相比，配置包含多少额外信息，有一些方法可以构建具有不同配置但相同的拟阵$\mathcal{G}$-不变的。我们提供了几种这样的结构以及用于开发更多的工具。