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

Simultaneous core partitions are important objects in algebraic combinatorics. Recently there has been interest in studying the distribution of sizes among all (s, t)-cores for coprime s and t. Zaleski (2017) gave strong evidence that when we restrict our attention to (s, s+1)-cores with distinct parts, the resulting distribution is approximately normal. We prove his conjecture by applying the Combinatorial Central Limit Theorem and mixing the resulting normal distributions.