未知偏序集上的秘书问题
The secretary problem on an unknown poset
摘要：
我们考虑的经典秘书问题，也被称为最优选择问题，偏序集的唯一信息，我们有偏序集的大小和极大元的数量的推广。我们表明，鉴于此信息，有一个算法，是成功的概率至少$\frac{1}{e}$。我们猜想，如果存在$k$极大元和$k \geq 2$，则可以将其改进为$\sqrt[k-1]{\frac{1}{k}}$，并证明了对于宽度为$k$的偏序集的这个猜想.我们还表明，没有更好的界限是可能的。
英文摘要：
We consider generalizations of the classical secretary problem, also known as the problem of optimal choice, to posets where the only information we have is the size of the poset and the number of maximal elements. We show that, given this information, there is an algorithm that is successful with probability at least $\frac{1}{e}$. We conjecture that if there are $k$ maximal elements and $k \geq 2$ then this can be improved to $\sqrt[k-1]{\frac{1}{k}}$, and prove this conjecture for posets of width $k$. We also show that no better bound is possible.
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。
