A Fast Fourier Transform for the Symmetric Group

Author

Tristan Brand, Harvey Mudd College

Graduation Year

2006

Document Type

Open Access Senior Thesis

Degree Name

Bachelor of Science

Department

Mathematics

Reader 1

Michael Orrison

Reader 2

Ghassan Sarkis (Pomona)

Abstract

A discrete Fourier transform, or DFT, is an isomorphism from a group algebra to a direct sum of matrix algebras. An algorithm that efficiently applies a DFT is called a fast Fourier transform, or FFT. The concept of a DFT will be introduced and examined from both a general and algebraic perspective. We will then present and analyze a specific FFT for the symmetric group.

Recommended Citation

Brand, Tristan, "A Fast Fourier Transform for the Symmetric Group" (2006). HMC Senior Theses. 179.
https://scholarship.claremont.edu/hmc_theses/179