Card shuffling and connections to representation theory

02/24/2009 - 12:15pm
02/24/2009 - 1:10pm
Lerna Pehlivan (University of Southern California)

We will study the distribution of the number of fixed points in a deck of cards which is top to random shuffled m times. We will find closed form expressions for the expectation and the variance of the number of fixed points. Both calculations are proved using the irreducible representations of symmetric groups. If time remains, we will also present other applications of irreducible representations in card shuffling problems.

ML 211