Parker vector - Alchetron, The Free Social Encyclopedia

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

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:

P k = k | G | ∑ g ∈ G c k ( g ) where c_k(g) is the number of k-cycles in the cycle decomposition of g.

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

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