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

Abstract

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 $t\ge 2$ 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.

arXiv comment23 pages