# Rachel Cranfill

## Thesis

Group Frames and Rank Data

Michael Orrison
In a finite-dimensional Hilber space $\mathcal{H}$, a frame is a spanning set of vectors. For a group $G$ with representation $\rho$, a frame can sometimes be constructed by fixing a vector in the Hilbert space and applying the images of all of the group elements under the representation. Such a frame is called a group frame. This thesis shows how group frames for the symmetric group $S_n$ can be used to explain certain “shortcuts” when testing for uniformity of rank data.