Graduation Year


Document Type

Open Access Senior Thesis

Degree Name

Bachelor of Science



Reader 1

Michael Orrison

Reader 2

Weiqing Gu


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.

emalm-2005-prop.pdf (65 kB)
Thesis Proposal

emalm-2004-10-12-ffts.pdf (605 kB)
10-Minute Thesis Presentation

emalm-2004-11-23-ffts.pdf (309 kB)
20-Minute Thesis Presentation

emalm-2005-01-08-ffts.pdf (231 kB)
DIF FFTs for the Symmetric Group

emalm-2005-04-17-ffts.pdf (245 kB)
Admitted Students Program

emalm-2005-05-02-ffts.pdf (414 kB)
Presentation Days Slides

emalm-2005-thesis-poster.pdf (275 kB)
Presentation Days Poster

emalm-2005-annbib.pdf (67 kB)

emalm-2005-expository.pdf (197 kB)
Recent Results in General FFTs

emalm-2005-midyear.pdf (429 kB)
Midyear Report

emalm-2005-prob-statement.pdf (30 kB)
Problem Statement

eric-malm-picture.jpg (26 kB)
Picture of Eric Malm