title: Parker vector
text: # 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:
  
      $P_{k}={\frac {k}{|G|}}\sum _{g\in G}c_{k}(g)$ where $c_k(g)$ is the number of k-cycles in the cycle decomposition of g.
  
  ## Applications
  
  The Parker vector can assist in the recognition of Galois groups.
  
  