Positivity Rigidity for Grossman-Larson Characters and the Kingman Face of the Hoffman Rooted-Tree Graph
Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Zhang, Shengjun
Institutions: Université Paris-Saclay, Laboratoire de Mathématiques d'Orsay
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214669390