Cutoff for the cyclic adjacent transposition shuffle

We study the cyclic adjacent transposition (CAT) shuffle of n cards, which is a systematic scan version of the random adjacent transposition (AT) card shuffle. In this paper, we prove that the CAT shuffle exhibits cutoff at n32.2logn, which concludes that it is twice as fast as the AT shuffle. This is the first verification of cutoff phenomenon for a time-inhomogeneous card shuffle.