Fast Fourier transforms for finite inverse semigroups

Martin E. Malandro
2010 Journal of Algebra  
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
more » ... and its wreath products by arbitrary finite groups.
doi:10.1016/j.jalgebra.2009.11.031 fatcat:ifzrvo6i45fxpn77jlu3r2b5ru