Hi Alex. Thank you for your reply! Maybe you’re not interested anymore, but here’s my solution for the special case of sampling a partition of kn numbers into n parts when k is fixed integer. Please see section 7 of this paper http://arxiv.org/abs/1504.06238
The expected running time is O(n^{3/2}). But we think it is possible to do it in O(n) time.

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