The asymptotic normality of \((s,s+1)\)-cores with distinct parts (Q2309223)

Summary: 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 \(t\). \textit{A. Zaleski} [Integers 19, Paper A26, 11 p. (2019; Zbl 1416.05036)] 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.