3 problems

Let $D70E_n$ be a uniformly random permutation in the symmetric group $D70E_n$, and let $D43E\operatorname{Pop}$ denote one step of Pop-Stack Sorting, which reverses every maximal…

For integers $m,t\geq 1$, let $h_t(m,n)$ denote the number of $t$-$\operatorname{\mathsf{Pop}}$-sortable $m$-ballot paths in the $m$-Tamari lattice $\operatorname{Tam}_n(m)$. Ratio…

Let $\mathsf{Pop}$ be the pop-stack-sorting map, which reverses every maximal decreasing run of a permutation, and let $\mathcal D_n^{\mathsf{Pop}}$ be the average number of iterat…