论文标题
关于增加和不变的停车序列
On Increasing and Invariant Parking Sequences
论文作者
论文摘要
停车序列的概念是Ehrenborg和Happ引入的停车功能的新概括。在定义经典停车功能的停车过程中，我们不仅要占用一个停车位，因此我们允许汽车具有不同的尺寸，并且在拖车$ t $ t $停放在第一个$ z-1 $ spots上的拖车之后，每辆车都占用了许多相邻的停车位。所有汽车都能停车的偏好序列称为停车序列。在本文中，我们研究了增加停车序列的增加，并通过将其进行对具有正确边界的晶格路径进行计数。然后，我们研究停车序列中的两个不变性概念，并提出各种特征和列举结果。
The notion of parking sequences is a new generalization of parking functions introduced by Ehrenborg and Happ. In the parking process defining the classical parking functions, instead of each car only taking one parking space, we allow the cars to have different sizes and each takes up a number of adjacent parking spaces after a trailer $T$ parked on the first $z-1$ spots. A preference sequence in which all the cars are able to park is called a parking sequence. In this paper, we study increasing parking sequences and count them via bijections to lattice paths with right boundaries. Then we study two notions of invariance in parking sequences and present various characterizations and enumerative results.
