Fast Fourier transforms for the rook monoid
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- by Martin Malandro and Dan Rockmore PDF
- Trans. Amer. Math. Soc. 362 (2010), 1009-1045 Request permission
Abstract:
We define the notion of the Fourier transform for the rook monoid (also called the symmetric inverse semigroup) and provide two efficient divide-and-conquer algorithms (fast Fourier transforms, or FFTs) for computing it. This paper marks the first extension of group FFTs to nongroup semigroups.References
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Additional Information
- Martin Malandro
- Affiliation: Department of Mathematics, 6188 Kemeny Hall, Dartmouth College, Hanover, New Hampshire 03755
- Address at time of publication: Department of Mathematics and Statistics, Sam Houston State University, Box 2206, Huntsville, Texas 77341-2206
- Email: malandro@shsu.edu
- Dan Rockmore
- Affiliation: Department of Mathematics, 6188 Kemeny Hall, Dartmouth College, Hanover, New Hampshire 03755
- Email: rockmore@cs.dartmouth.edu
- Received by editor(s): September 25, 2007
- Received by editor(s) in revised form: June 2, 2008
- Published electronically: September 17, 2009
- Additional Notes: The first author was supported by a graduate fellowship.
The second author was supported by AFOSR under grant FA9550-06-1-0027. - © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 362 (2010), 1009-1045
- MSC (2000): Primary 20C40, 20M18, 43A30; Secondary 20M30, 68W40
- DOI: https://doi.org/10.1090/S0002-9947-09-04838-7
- MathSciNet review: 2551514