标题： 彩色高斯模型的二项性 显示英文标题

标题： Binomiality of colored Gaussian models

摘要： 根据Coons-Maraj-Misra-Sorea和Misra-Sullivant的前期工作，我们研究了着色的、无向的高斯图模型，并提出了这种模型具有二项式消去理想的充要条件。 这些条件涉及Jordan方案，一种关联方案的变体，在代数组合学中是众所周知的结构。 使用没有传递群作用的关联方案，我们驳斥了Coons-Maraj-Misra-Sorea提出的猜想，即二项式性意味着颜色类必须是着色图自同构群下的轨道。 显示英文摘要

摘要： Following earlier work by Coons-Maraj-Misra-Sorea and Misra-Sullivant, we study colored, undirected Gaussian graphical models, and present a necessary and sufficient condition for such a model to have binomial vanishing ideal. These conditions involve Jordan schemes, a variant of association schemes, well-known structures in algebraic combinatorics. Using association schemes without transitive group action, we refute the conjecture by Coons-Maraj-Misra-Sorea that binomiality implies that the color classes must be orbits under the automorphism group of the colored graph.