The asymptotic normality of $(s,s+1)$-cores with distinct parts

Sizes of Simultaneous Core Partitions

“…The enumeration of restricted partitions has been established in various cases, as well as their maximum and average size, and some higher moments. Remarkably, the size distribution of (s, s + 1) core partitions into distinct parts has been shown to be asymptotically normal [KST18]. While Theorem 0.1 settles the asymptotics of the fundamental case of general (s, t)-core partitions, the formula in Proposition 0.2 is applicable also to restricted cases, such as those mentioned above.…”