AI 中文总结
本文分类了 Grossman-Larson Hopf 代数在根树基上的非负实特征，揭示其由 Kingman paintbox 参数化，并刻画了 Hoffman 根树图上的中心测度面及 Martin 边界结构。
AI 中文摘要
我们分类了 Grossman-Larson Hopf 代数中在根树基上非负的实特征。这些特征在远离根部分支的树上为零，且归一化特征由 Kingman paintbox 参数化。双侧 Pieri 态是归一化特征的混合，具有唯一的混合测度。相应的分布形成了 Hoffman 根树图上中心测度单纯形的一个真暴露 Bauer 面。对于路径森林子图，完全 Martin 边界与最小 Martin 边界重合，且同胚于 Kingman 单纯形。极限的排序根分支频率生成了完整的中心尾部。
英文摘要
We classify the real characters of the Grossman-Larson Hopf algebra that are nonnegative on the rooted-tree basis. They vanish on trees with branching away from the root, and the normalized characters are parametrized by Kingman paintboxes. Two-sided Pieri states are mixtures of the normalized characters, with unique mixing measures. The corresponding laws form a proper exposed Bauer face of the simplex of central measures on the Hoffman rooted-tree graph. For the path-forest subgraph, the full and minimal Martin boundaries coincide and are homeomorphic to the Kingman simplex. The limiting ranked root-branch frequencies generate the completed central tail.
Comments26 pages, 2 figures
