Abstract The prefix exchange distance of a permutation is the length of its shortest factorisation into transpositions that all contain 1. Using a probabilistic approach, we obtain expressions for the mean and the variance, and prove the asymptotic normality of the distribution of this distance for a random permutation verifying the Ewens sampling formula. Analogous results in the uniform setting follow as simple corollaries.

中文翻译：

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Ewens采样公式下前缀交换距离的中心极限定理

摘要 置换的前缀交换距离是其最短因式分解为所有包含 1 的转置的长度。使用概率方法，我们获得均值和方差的表达式，并证明该距离分布的渐近正态性验证 Ewens 抽样公式的随机排列。统一设置中的类似结果是简单的推论。