A ladder lottery, known as ``Amidakuji'' in Japan, is a common way to decide an assignment at random. In this paper, we investigate reconfiguration and enumeration problems of cyclic ladder lotteries. First, when a permutation $\pi$ and an optimal displacement vector $\bm{x}$ are given, we investigate the reconfiguration and enumeration problems of the ``optimal'' cyclic ladder lotteries of $\pi$ and $\bm{x}$. Next, for a give permutation $\pi$ we consider reconfiguration and enumeration problems of the optimal displacement vectors of $\pi$.

翻译：梯子彩票（在日本称为“Amidakuji”）是一种常见的随机分配方式。本文研究了循环梯子彩票的重构与枚举问题。首先，给定一个排列 $\pi$ 和一个最优位移向量 $\bm{x}$，我们研究了 $\pi$ 和 $\bm{x}$ 的“最优”循环梯子彩票的重构与枚举问题。其次，对于给定的排列 $\pi$，我们考虑了 $\pi$ 的最优位移向量的重构与枚举问题。