Honors Project On-Campus Access Only
This paper aims to build connections between representation theory and signal processing. We consider ranked voting data, such as when voters rank n candidates or when users rank n movies. Each ranking is a permutation, and the total count of votes for each permutation can be viewed as a vector on the permutohedron. In order to analyze this data using techniques from graph signal processing, it is helpful to understand the eigenvalues and eigenvectors of the permutohedron and other Cayley graphs of the symmetric group. We use tools from representation theory to reduce the problem of computing n! eigenvalues and vectors to computations in smaller matrices, and we use methods from graph signal processing to find partisan patterns in the voting data.
Li, Zhaoqi, "Spectra of Cayley Graphs of the Symmetric Group" (2018). Mathematics, Statistics, and Computer Science Honors Projects. 38.
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