发表机构
Grinnell College; University of Colorado–Boulder（格林内尔学院; 科罗拉多大学博尔德分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究树形偏序集上的转移系统，证明其与有界保序函数一一对应，并给出递推枚举方法；同时证明对偶偏序集上的转移系统格与原格对偶同构，通过弱因子分解系统建立联系。
AI 中文摘要
我们研究了Hasse图为有根树的偏序集上的转移系统。我们证明了树上的转移系统与受秩函数约束的、到自然数的保序函数之间存在一一对应关系。随后，我们为这类函数集发展了一个递推关系，并利用它枚举了若干树族上的转移系统。除树的研究外，我们还证明了对于任何有限偏序集 $\mathcal{P}$，其对偶偏序集 $\mathcal{P}^{op}$ 上的转移系统格与 $\mathcal{P}$ 上的转移系统格的对偶格同构。我们通过建立弱因子分解系统与转移系统之间的一一对应关系来证明这一点，该对应关系基于Franchere、Ormsby、Osorno、Qin和Waugh先前工作中关于格的结果。
英文摘要
We study transfer systems on partially ordered sets whose Hasse diagrams are rooted trees. We prove there is a bijection between transfer systems on a tree and order-preserving functions to the natural numbers that are bounded by the rank function. We then develop a recurrence for the set of functions and use this to enumerate transfer systems on some families of trees. In addition to our study of trees, we prove for any finite poset $\mathcal{P}$, the lattice of transfer systems on the opposite poset $\mathcal{P}^{op}$ is isomorphic to the opposite lattice of transfer systems on $\mathcal{P}$. We show this by establishing a bijection between weak factorization systems and transfer systems, which builds on the results for lattices shown in previous work of Franchere, Ormsby, Osorno, Qin, and Waugh.
