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Fragmenting random permutations

   
@article{ECP1402,
	author = {Christina Goldschmidt and James Martin and Dario Spano},
	title = {Fragmenting random permutations},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {13},
	year = {2008},
	keywords = {Fragmentation process, random permutation, Gibbs partition, Chinese restaurant process},
	abstract = {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.},
	pages = {no. 44, 461-474},
	issn = {1083-589X},
	doi = {10.1214/ECP.v13-1402},    
        url = {http://ecp.ejpecp.org/article/view/1402}}