Cutoff for a one-sided transposition shuffle

We introduce a new type of card shuffle called one-sided transpositions. At each step is chosen uniformly from the pack and then transposed with another below it. This defines random walk on symmetric group generated by distribution which nonconstant conjugacy class Nevertheless, we provide an explicit formula for all eigenvalues demonstrating useful correspondence between standard Young tableaux. allows us to prove existence total-variation cutoff transposition at time nlogn. also study weighted generalisation which, in particular, recover well-known mixing classical shuffle.