Author (Your Name)

Qidong HeFollow

Date of Award


Document Type

Honors Thesis (Open Access)


Colby College. Mathematics and Statistics Dept.


Tamar Friedmann

Second Advisor

Fernando Gouvêa


Given a compact exceptional group $G$ and $m,s\in\mathbb{N}$, let $N(G,m)$ be the number of conjugacy classes of elements of order $m$ in $G$, and $N(G,m,s)$ the number of such classes whose elements have $s$ distinct eigenvalues. In string theory, the problem of enumerating certain classes of vacua in the string landscape can be rephrased in terms of the study of these quantities. We develop unified combinatorial algorithms based on Burnside's Lemma that can be used to compute both quantities for each of the five compact exceptional groups. Thus, we provide a combinatorial, alternative method to that of Djoković and extend previous results obtained by Friedmann-Stanley for the compact classical groups.


Conjugacy classes, finite order, Lie groups, Burnside's Lemma, Möbius inversion