Open Access Senior Thesis
Bachelor of Science
In this thesis, we present a new class of algorithms that determine fast Fourier transforms for a given finite group G. These algorithms use eigenspace projections determined by a chain of subgroups of G, and rely on a path algebraic approach to the representation theory of finite groups developed by Ram (26). Applying this framework to the symmetric group, Sn, yields a class of fast Fourier transforms that we conjecture to run in O(n2n!) time. We also discuss several future directions for this research.
Malm, Eric, "Decimation-in-Frequency Fast Fourier Transforms for the Symmetric Group" (2005). HMC Senior Theses. 173.