Shuffling via transpositions

In their seminal work, Diaconis and Shahshahani proved that shuffling a deck of $n$ cards sufficiently well via random transpositions takes $\frac{1}{2} n \log n$ steps. Their argument was algebraic and relied on the combinatorics of the symmetric group. In this talk, I will focus on a generalization of random transpositions and I will discuss the underlying combinatorics for understanding their mixing behavior and indeed proving cutoff. The talk will be based on joint work with S. Arfaee.

For information about the Richard P. Stanley Seminar in Combinatorics, visit https://math.mit.edu/combin/