论文标题
在有向星的停车功能和定向逆转，并扩展到一般有向树
Parking functions on directed stars and orientation reversal with an extension to general directed trees
论文作者
论文摘要
停车功能是在试图停放在此处的定向路径上的汽车上经常定义的，在许多组合情况下出现，并看到了各种概括。特别是，已定义了通用挖掘物的停车功能，这会产生更多的枚举问题。例如，在一个有向的树中，其边缘从根而定向，一般来说，即使在树是恒星的情况下，一旦方向逆转，停车功能的数量是如何变化的。我们表明，在大多数情况下，这种定向逆转会导致对定向恒星的更多停车功能，此后我们扩展了这些方法，以表明，如果从某种意义上说，这也会在一般的定向树上产生更多的停车功能，那么顶点的数量大大超过了汽车的数量。
Parking functions, classically defined in terms of cars with preferred parking spots on a directed path attempting to park there, arise in many combinatorial situations and have seen various generalizations. In particular, parking functions have been defined for general digraphs, which yields many more enumeration problems. For example, in a directed tree whose edges are orientated away from the root, it is unknown in general how the number of parking functions on it changes once the orientation is reversed, even in the case when the tree is a star. We show that this orientation reversal results in more parking functions on the directed star in most cases, after which we extend these methods to show that this also results in more parking functions on the general directed tree if, in some sense, the number of vertices greatly exceeds the number of cars.
