Hook length biases for self-conjugate partitions and partitions with distinct odd parts

We establish a hook length bias between self-conjugate partitions and partitions of distinct odd parts, demonstrating that there are more hooks of fixed length t ≥ 2 among self-conjugate partitions of n than among partitions of distinct odd parts of n for sufficiently large n. More precisely, we derive asymptotic formulas for the total number of hooks of fixed length t in both classes. This resolves a conjecture of Ballantine, Burson, Craig, Folsom, and Wen.