Fast Fourier Transforms for Finite Inverse Semigroups
نویسنده
چکیده
We extend the theory of fast Fourier transforms on finite groups to finite inverse semigroups. We use a general method for constructing the irreducible representations of a finite inverse semigroup to reduce the problem of computing its Fourier transform to the problems of computing Fourier transforms on its maximal subgroups and a fast zeta transform on its poset structure. We then exhibit explicit fast algorithms for particular inverse semigroups of interest—specifically, for the rook monoid and its wreath products by arbitrary finite groups.
منابع مشابه
Fast Fourier Transforms for Inverse Semigroups
In this thesis, we develop a theory of Fourier analysis and fast Fourier transforms (FFTs) for finite inverse semigroups. Our results generalize results in the theory of Fourier analysis for finite groups. There is a general method for generating the irreducible representations of an inverse semigroup, and we use this method to prove that the problem of creating FFTs for inverse semigroups can ...
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