2 problems

Consider the adjacent-swap Markov chain on unlabeled ranked tree shapes, whose states are represented by ordered matchings and whose moves swap allowable labels in adjacent pairs.…

Let $t_n$ and $t_n^L$ denote the mixing times of the adjacent-swap Markov chains on the spaces $4\mathcal{T}_n$ and $4\mathcal{T}_n^L$ of unlabeled and leaf-labeled ranked tree sha…