The Asymptotic Normality of $(s,s+1)$-Cores with Distinct Parts

  • János Komlós
  • Emily Sergel
  • Gábor Tusnády


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.

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