Abstract A triangular matroid is a rank-3 matroid whose ground set consists of the points of an n 3 {n}_{3} -configuration and whose bases are the point triples corresponding to non-triangles within the configuration. Raney previously enumerated the n 3 {n}_{3} -configurations which induce triangular matroids for 7 ≤ n ≤ 15 7\le n\le 15 . In this work, the enumeration is extended to configurations having up to 18 points. Several examples of such configurations and their symmetry groups are presented, as well as geometric representations of the triangular matroids induced by these configurations.

中文翻译：

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关于由 n 3-配置引起的三角拟阵

摘要 三角拟阵是一个秩为3的拟阵，其基集由n 3 {n}_{3}-构型的点组成，其基是与构型中的非三角形对应的点三元组。Raney 之前列举了 n 3 {n}_{3} - 构型，这些构型导致 7 ≤ n ≤ 15 7\le n\le 15 的三角拟阵。在这项工作中，枚举扩展到最多 18 个点的配置。介绍了这种配置及其对称群的几个例子，以及由这些配置引起的三角形拟阵的几何表示。