4 problems

Defant's conjecture.

Defant's conjecture. For every fixed $t$, the generating function $\sum_{n\ge 1} h_t(n)z^n$ is rational. This is a conjecture about enumerating iterated pop-stack-sortable elements…

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…