Wilson loop diagrams are an important tool in studying scattering amplitudes of SYM $N=4$ theory and are known by previous work to be associated to positroids. We characterize the conditions under which two Wilson loop diagrams give the same positroid, prove that an important subclass of subdiagrams (exact subdiagrams) corresponds to uniform matroids, and enumerate the number of different Wilson loop diagrams that correspond to each positroid cell. We also give a correspondence between those positroids which can arise from Wilson loop diagrams and directions in associahedra.

中文翻译：

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威尔逊环图几何的组合 I：通过拟阵和多面体的等价类

威尔逊环图是研究 SYM $N=4$ 理论的散射幅度的重要工具，并且在以前的工作中已知与正类相关。我们描述了两个威尔逊环图给出相同正态的条件，证明子图的一个重要子类（精确子图）对应于均匀拟阵，并列举了对应于每个正态单元的不同威尔逊环图的数量。我们还给出了可能从威尔逊环图和关联面中的方向产生的那些正类之间的对应关系。