偏序集的重序比
The Reversal Ratio of a Poset
摘要：
Felsner和Schmidt引入了偏序集$\mathbf{P}$的线性扩张直径，记为$\mbox{led}(\mathbf{P})$，作为$\mathbf{P}$的两个线性扩张之间的最大距离，其中距离定义为线性扩张中出现相反顺序（反向）的不可比对的数量。本文引入了$\mathbf{P}$的反转比$RR(\mathbf{P})$作为线性扩张直径与（无序）不可比对数目的比值。我们使用概率技术，以提供一个家庭的偏序集$\mathbf{P}_k$在大多数$k\log k$元素的反转比$RR(\mathbf{P}_k)\leq C/\log k$，其中$C$是一个常数。我们还研究了在订单尺寸和宽度方面限制反转率的问题。
英文摘要：
Felsner and Reuter introduced the linear extension diameter of a partially ordered set $\mathbf{P}$, denoted $\mbox{led}(\mathbf{P})$, as the maximum distance between two linear extensions of $\mathbf{P}$, where distance is defined to be the number of incomparable pairs appearing in opposite orders (reversed) in the linear extensions. In this paper, we introduce the reversal ratio $RR(\mathbf{P})$ of $\mathbf{P}$ as the ratio of the linear extension diameter to the number of (unordered) incomparable pairs. We use probabilistic techniques to provide a family of posets $\mathbf{P}_k$ on at most $k\log k$ elements for which the reversal ratio $RR(\mathbf{P}_k)\leq C/\log k$, where $C$ is a constant. We also examine the questions of bounding the reversal ratio in terms of order dimension and width.
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。
