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Fast Fourier transforms for symmetric groups: theory and implementation

Authors: Michael Clausen and Ulrich Baum
Journal: Math. Comp. 61 (1993), 833-847
MSC: Primary 20C40; Secondary 20C30, 68Q40
MathSciNet review: 1192969
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Abstract: Recently, it has been proved that a Fourier transform for the symmetric group $ {S_n}$ based on Young's seminormal form can be evaluated in less than $ 0.5({n^3} + {n^2})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.

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Article copyright: © Copyright 1993 American Mathematical Society

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