I imagine someone has studied this already so I'm just looking for resources: what sort of asymptotic behavior does the distribution of integer partitions of $n$ counted by the number of parts exhibit? Looking at the plots that WolframAlpha supplies for low-ish values (around 30), the distribution looks sort of like Tracy-Widom.
2026-04-01 19:39:06.1775072346
Distribution of integer partitions by number of parts
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