Ballantine–Burson–Craig–Folsom–Wen hook-count conjecture

Let $a_t(n)$ be the total number of $t$-hooks in all partitions of $n$ into odd parts, and let $b_t(n)$ be the total number of $t$-hooks in all partitions of $n$ into distinct parts. For $n\geq 1$, one has $\sum_{t\geq 1}a_t(n)=\sum_{t\geq 1}b_t(n)$, and Andrews's inequality gives $a_1(n)\geq b_1(n)$. Ballantine–Burson–Craig–Folsom–Wen conjecture. For every integer $t\geq 2$,

$$a_t(n)-b_t(n)\to\infty \quad\text{as }n\to\infty.$$

The conjecture reverses Andrews's inequality for every hook length $t>1$ in the asymptotic sense. It was proved for $t=2,3$ by Ballantine, Burson, Craig, Folsom, and Wen, and the remaining cases were settled by Craig, Dawsey, and Han.