标题： 关于$k$-那不勒斯停车函数和停车策略的组合学 显示英文标题

标题： On the combinatorics of $k$-Naples parking functions and parking strategies

摘要： 我们提出了一种关于$k$-那不勒斯停车函数的表征，该表征基于具有完整$k$-那不勒斯停车函数结构的子序列。 我们通过要求对于所有$j=2,\dots,n$，拥有至少$j$偏好的车辆数量严格大于$[j,n]$中的车位数量，定义了完整的停车偏好。 我们还提供了关于排列不变的$k$-那不勒斯停车函数的表征。 最后，我们引入了停车问题的一个推广，其中每辆车都有自己的停车规则，通过将停车策略定义为允许所有车辆停车的规则向量。 给定一个停车偏好，我们还研究了找到最小化某些自然参数的停车策略的方法，例如总的后退步骤数，或需要后退行驶的车辆数量。 显示英文摘要

摘要： We propose a characterization of $k$-Naples parking functions in terms of subsequences with the structure of a complete $k$-Naples parking function. We define complete parking preferences by requiring that for all $j=2,\dots,n$, the number of cars having preference at least $j$ is strictly greater than the number of spots in $[j,n]$. We also provide a characterization of permutation invariant $k$-Naples parking functions. Finally, we introduce a generalization of the parking problem where each car is given its own parking rule, by defining parking strategies as vectors of rules that allow all cars to park. Given a parking preference, we also investigate ways to find parking strategies that minimize certain natural parameters, such as the total number of backward steps, or the number of cars that need to drive backwards.