k缺陷偏好集
k-flaw Preference Sets
摘要：
本文用$\mathcal{P}_{n;\leq s;k}^l$表示一个$k$ -缺陷偏好集$(a_1,...,a_n)$，其中$n$的停车空间满足$1\leq a_i\leq s$，对于任何$i$和$a_1=l$和$p_{n;\leq s;k}^l=|\mathcal{P}_{n;\leq s;k}^l|$ .我们使用一种组合的方法来枚举的$k$缺陷偏好集的首项。该方法依赖于双射之间的$k$缺陷偏好集和标记的根森林。给出了不同首项的某些$k$ -缺陷偏好集之间的双射结果。本文导出了序列$p_{n;\leq s;k}^l$的一些公式和递推关系，并给出了这类序列的生成函数。
英文摘要：
In this paper, let $\mathcal{P}_{n;\leq s;k}^l$ denote a set of $k$-flaw preference sets $(a_1,...,a_n)$ with $n$ parking spaces satisfying that $1\leq a_i\leq s$ for any $i$ and $a_1=l$ and $p_{n;\leq s;k}^l=|\mathcal{P}_{n;\leq s;k}^l|$. We use a combinatorial approach to the enumeration of $k$-flaw preference sets by their leading terms. The approach relies on bijections between the $k$-flaw preference sets and labeled rooted forests. Some bijective results between certain sets of $k$-flaw preference sets of distinct leading terms are also given. We derive some formulas and recurrence relations for the sequences $p_{n;\leq s;k}^l$ and give the generating functions for these sequences.
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。
