2 problems

For integers $k\leq n$, let $U_k(n)$ be the minimum length of a sequence of independent lazy transpositions whose product maps the elements $1,\dots,k$ uniformly to the…

Let $U(n)$ denote the minimum number of independent lazy transpositions whose product is a uniformly random permutation of $n$ elements. Groenland, Johnston, Radcliffe and Scott's…