It's not super obvious. And, truthfully, it doesn't actually make any difference worth noting. However, a PhD dissertation is your chance to get things really right, so being picky is in order.
The problem with this derivation is that we take as the probability that a block partition comes from partition m as the ratio of the rows in partition m to the total rows. That's not a bad approximation but, the rest of the formula is really specific, so approximating this term isn't appropriate.
It should be the marginal distribution, P(m|k), rather than just P(m). For a given value of m, that's quite different. In total it washes out a bit, but not completely.
This is the sort of semantic stuff that I'm not super good at. It's not that I don't think it's important; it's just that I tend to miss these things. I hope my adviser is good at catching them.
Anyway, I've updated the sampler to reflect the correct term.
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