46.18 PowerPartition

PowerPartition( pi, k )

returns the partition corresponding to the k-th power of a permutation with cycle structure pi.

    gap> PowerPartition([6,5,4,3,2,1], 3);
    [ 5, 4, 2, 2, 2, 2, 1, 1, 1, 1 ]

Each part l of pi is replaced by d = gcd(l, k) parts l/d. So if pi is a partition of n then <pi>^{<k>} also is a partition of n. PowerPartition describes the powermap of symmetric groups.

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