On the distribution of t-hooks of doubled distinct partitions

Abstract

Recently, Griffin, Ono, and Tsai examined the distribution of the number of t-hooks in partitions of n, which was later followed by the work of Craig, Ono, and Singh on the distribution of the number of t-hooks in self-conjugate partitions of n. Motivated by these studies, in this paper, we further investigate the number of t-hooks in some subsets of partitions. More specifically, we obtain the generating functions for the number of t-hooks in doubled distinct partitions and the number of t-shifted hooks in strict partitions. Based on these generating functions, we prove that the number of t-hooks in doubled distinct partitions and the number of t-shifted hooks in strict partitions are both asymptotically normally distributed.