3 problems

Joint-growth height conjecture. As $\min(n,m)\to\infty$,

Fixed-block-height conjecture. When $n$ is fixed and $m\to\infty$, the properly rescaled height converges to $c^*H_n^{(1)}$, where $c^*\approx 4.311$ is the constant from Devroye's…

Let $n>6$, let $(\lambda,\mu)\models n$ with $\ell(\lambda)\geq 2$, and let $W_k^{\lambda,\mu}$ denote the quantity associated with component-type $(\lambda,\mu)$ and parameter $k$…