C Goldschmidt, JB Martin and D Spano
Fragmenting random permutations
Abstract: Problem 1.5.7 from Pitman’s Saint-Flour lecture notes : Does there exist for each n a Pn-valued fragmentation process (_n,k, 1 _ k _ n) such that _n,k is distributed like the partition generated by cycles of a uniform random permutation of [n] conditioned to have k cycles? We show that the answer is yes. We also give a partial extension to general exchangeable Gibbs partitions.