Parker vector

From Wikipedia, the free 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.

Contents 1 Definition 2 Examples 3 Applications 4 References

[edit] Definition

Please help improve this section by expanding it. Further information might be found on the talk page or at requests for expansion.

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

[edit] Examples

Please help improve this section by expanding it. Further information might be found on the talk page or at requests for expansion.

[edit] Applications

Please help improve this section by expanding it. Further information might be found on the talk page or at requests for expansion.

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

[edit] References

• Peter J. Cameron (1999). Permutation Groups. Cambridge University Press. ISBN 0521653789. 
• Aart Blokhuis (2001). Finite Geometries: Proceedings of the Fourth Isle of Thorns Conference. Springer. ISBN 0792369947. 

This article or section is in need of attention from an expert on the subject. WikiProject Mathematics or the Mathematics Portal may be able to help recruit one. If a more appropriate WikiProject or portal exists, please adjust this template accordingly.