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Recently, it has been proved that a Fourier transform for the symmetric group S, based on Young's seminormal form can be evaluated in less than 0.5(n3 + n2)n! arithmetic operations. We look at this algorithm in more detail and show that it allows an efficient software implementation using appropriate data structures. We also describe a similarly efficient algorithm for the inverse Fourier transform. We compare the time and memory requirements of our program to those of other existing implementations.

Fast Fourier transforms for symmetric groups: theory and implementation