Fast Fourier Transforms for the Rook Monoid

Details Fast Fourier Transforms for the Rook Monoid Fast Fourier Transforms for the Rook Monoid

2007-09-26

arxiv.org/abs/0709.4175v1

Trans. Amer. Math. Soc. 362 (2010), 1009-1045

Mathematics

Representation Theory

Scientific paper

10.1090/S0002-9947-09-04838-7

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 non-group semigroups.

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