Parker vector

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In mathematics, especially the field of group theory, the Parker vector is an integer vector that describes a permutation group in terms of the cycle structure of its elements.

Definition[edit]

The Parker vector P of a permutation group G acting on a set of size n, is the vector whose kth component for k = 1, …, n is given by:

where ck(g) is the number of k-cycles in the cycle decomposition of g.

Applications[edit]

The Parker vector can assist in the recognition of Galois groups.

References[edit]