Card shuffling and a transformation on S n

Abstract

We consider two card shuffling schemes. The first, which has appeared in the literature previously ([G], [RB], [T]), is as follows: start with a deck ofn cards, and pick a random tuplet ∈ { 1, 2, ⋯, n} n ; interchange cards 1 andt1, then interchange cards 2 andt2, etc. The second scheme, which can be viewed as a transformation on the symmetric groupS n , is given by the restriction of the former shuffling scheme to tuplest which form a permutation of {1, 2,⋯,n}.