停车函数的非期望空间分解
A Decomposition of Parking Functions by Undesired Spaces
摘要：
有一个众所周知的双射之间的停车功能的一个固定的长度和最大链的非交叉分划格，我们可以用来关联到每一组停车功能的偏序集，其哈斯图是相应的最大链的联合。本文引入了一种基于最大省略数的停车函数的分解，并证明了几个关于相应偏序集的定理。特别是，它们与非交叉分划格共享属性，例如局部自对偶性，区间的良好表征，易于计算的默比乌斯函数和对称链分解。我们还探讨了与秩序复合体，标记戴克路径和扎根森林的连接。
英文摘要：
There is a well-known bijection between parking functions of a fixed length and maximal chains of the noncrossing partition lattice which we can use to associate to each set of parking functions a poset whose Hasse diagram is the union of the corresponding maximal chains. We introduce a decomposition of parking functions based on the largest number omitted and prove several theorems about the corresponding posets. In particular, they share properties with the noncrossing partition lattice such as local self-duality, a nice characterization of intervals, a readily computable Möbius function, and a symmetric chain decomposition. We also explore connections with order complexes, labeled Dyck paths, and rooted forests.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
