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

David Maslan (1) , Daniel N. Rockmore (2) , Sarah Wolff (3)

1 HBK - HBK Capital Management
2 Department of Mathematics [Dartmouth]
3 Department of Mathematics and Computer Science [Granville]

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

Mots clés: Combinatorics

Domaines: Combinatoire [math.CO]

David Maslan, Daniel N. Rockmore, Sarah Wolff. Separation of Variables and the Computation of Fourier Transforms on Finite Groups, II. 28-th International Conference on Formal Power Series and Algebraic Combinatorics, Simon Fraser University, Jul 2016, Vancouver, Canada. ⟨10.46298/dmtcs.6372⟩. ⟨hal-02166353⟩