Pop-Stack Sorting is an algorithm that takes a permutation as an input and sorts its elements. It consists of several steps. At one step, the algorithm reads the permutation it has to process from left to right and reverses each of its maximal decreasing subsequences of consecutive elements. It terminates at the first step that outputs the identity permutation. In this note, we answer a question of Defant on the running time of Pop-Stack Sorting on the uniform random permutation $\sigma_n$. More precisely, we show that there is a constant $c > 0.5$ such that asymptotically almost surely, the algorithm needs at least $cn$ steps to terminate on $\sigma_n$.

翻译：popp- Stack 排序是一种算法, 其输入和排序其元素。 它由多个步骤组成。 一步, 算法读取它从左到右处理的变异, 并反转它每个最大递减的连续元素子序列。 它在输出身份变异的第一个步骤就终止了 。 在本说明中, 我们回答一个问题, 即对 Pop- stack 运行时间进行调整时对统一随机变换 $\ sigma_ n$ 。 更确切地说, 我们显示, 常值 $ > 0. 5 美元, 也就是说, 算法需要至少 $\ sigma_ n$ 来终止 。