DOAJ Open Access 2020

Separation of Variables and the Computation of Fourier Transforms on Finite Groups, II

David Maslan Daniel N. Rockmore Sarah Wolff

Lihat Sumber DOI

Abstrak

We present a general diagrammatic approach to the construction of efficient algorithms for computingthe Fourier transform of a function on a finite group. By extending work which connects Bratteli diagrams to theconstruction of Fast Fourier Transform algorithms we make explicit use of the path algebra connection and work inthe setting of quivers. In this setting the complexity of an algorithm for computing a Fourier transform reduces to pathcounting in the Bratelli diagram, and we generalize Stanley's work on differential posets to provide such counts. Ourmethods give improved upper bounds for computing the Fourier transform for the general linear groups over finitefields, the classical Weyl groups, and homogeneous spaces of finite groups.

Topik & Kata Kunci

Mathematics

Penulis (3)

David Maslan

Daniel N. Rockmore

Sarah Wolff

Format Sitasi

APA MLA BibTeX

Maslan, D., Rockmore, D.N., Wolff, S. (2020). Separation of Variables and the Computation of Fourier Transforms on Finite Groups, II. https://doi.org/10.46298/dmtcs.6372

Akses Cepat

Lihat di Sumber doi.org/10.46298/dmtcs.6372

Informasi Jurnal

Tahun Terbit: 2020
Sumber Database: DOAJ
DOI: 10.46298/dmtcs.6372
Akses: Open Access ✓