Problem 1.5.7 from Pitman's Saint-Flour lecture notes: Does there exist for each $n$ a fragmentation process $(Pi_{n,k}, 1 leq k leq n)$ such that $Pi_{n,k}$ is distributed like the partition generated by cycles of a uniform random permutation of ${1,2,ldots,n}$ conditioned to have $k$ cycles? We show that the answer is yes. We also give a partial extension to general exchangeable Gibbs partitions.
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机译：Pitman的Saint-Flour讲座的问题1.5.7指出：每个$ n $是否都存在一个碎片化过程$（ Pi_ {n，k}，1 leq k leq n）$，使得$ Pi_ {n， k} $的分布就像由条件为具有$ k $个周期的$ {1,2， ldots，n } $的均匀随机置换周期产生的分区一样？我们证明答案是肯定的。我们还对通用的可交换Gibbs分区进行了部分扩展。
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