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. In this paper, we study the structure of the associated positroids, as well as the structure of the denominator of the integrand defined by each diagram. We give an algorithm to derive the Grassmann necklace of the associated positroid directly from the Wilson loop diagram, and a recursive proof that the dimension of these cells is thrice the number of propagators in the diagram. We also show that the ideal generated by the denominator in the integrand is the radical of the ideal generated by the product of Grassmann necklace minors.

威尔逊环图是研究 SYM $N=4$ 理论的散射振幅的重要工具，之前的工作已知它与正极体相关。在这篇论文中，我们研究了相关的positroids的结构，以及每个图定义的被积函数的分母的结构。我们给出了一种算法，可以直接从 Wilson 回路图导出相关正极体的 Grassmann 项链，并递归证明这些单元的维数是图中传播子数量的三倍。我们还表明，被积函数中的分母生成的理想是格拉斯曼项链未成年人的乘积生成的理想的根。