Reconfiguration and enumeration of optimal cyclic ladder lotteries

Abstract

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 π and an optimal displacement vector x are given, we investigate the reconfiguration and enumeration problems of the “optimal” cyclic ladder lotteries of π and x. Next, for a given permutation π we consider reconfiguration and enumeration problems of the optimal displacement vectors of π.