# Parker vector

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:

${\displaystyle P_{k}={\frac {k}{|G|}}\sum _{g\in G}c_{k}(g)}$ where ck(g) is the number of k-cycles in the cycle decomposition of g.

## Applications

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