There is a well-studied correspondence by Jaclyn Anderson between partitions that avoid hooks of length s or t and certain binary strings of length $s+t$. Using this map, we prove that the total size of a random partition of this kind converges in law to Watson's $U^2$ distribution, as conjectured by Doron Zeilberger.

中文翻译：

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并发核心分区的大小

Jaclyn Anderson 对避免长度为s或t 的钩子的分区与某些长度的二进制字符串之间的对应关系进行了深入研究$秒+吨$. 使用此映射，我们证明这种随机分区的总大小在法律上收敛到 Watson 的${你}^2$ 分布，正如 Doron Zeilberger 所推测的那样。