Recent work has shown that fast matrix multiplication algorithms can be constructed by embedding the two input matrices into a group algebra, applying a generalized discrete Fourier transform, and performing the multiplication in the Fourier basis. Developing an embedding that yields a matrix multiplication algorithm with running time faster than naive matrix multiplication leads to interesting combinatorial problems in group theory. The crux of such an embedding, after a group G has been chosen, lies in finding a triple of subsets of G that satisfy a certain algebraic relation. I show how the process of finding such subsets can in some cases be greatly simplified by considering the action of the group G on an appropriate set X. In particular, I focus on groups acting on regularly branching trees.
| Identifer | oai:union.ndltd.org:CLAREMONT/oai:scholarship.claremont.edu:hmc_theses-1224 |
| Date | 01 May 2009 |
| Creators | Orem, Hendrik |
| Publisher | Scholarship @ Claremont |
| Source Sets | Claremont Colleges |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | HMC Senior Theses |
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