Singh–Barman's hook bias conjecture for 3-regular partitions

Let $b_{t,i}(n)$ denote the number of hooks of length $i$ in all $t$-regular partitions of $n$. Singh–Barman's conjecture. For all $n\ge 28$, $b_{3,2}(n)\ge b_{3,1}(n)$.

This conjecture concerns the bias between hooks of lengths two and one in 3-regular partitions. The paper states that its first main result confirms the conjecture, so it is solved.