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.

gollark: Sadly, it checks against the maximum year on all operations for some stupid reason.

gollark: In C modules, so I can't even patch it.

gollark: It's hardcoded.

gollark: The limit is exactly the year 9999.

gollark: Python has an annoying limitation where times above 9999 years are artificially blocked.

References

Peter J. Cameron (1999). Permutation Groups. Cambridge University Press. p. 48. ISBN 0-521-65378-9. Parker Vector.
Aart Blokhuis (2001). Finite Geometries: Proceedings of the Fourth Isle of Thorns Conference. Springer. ISBN 0-7923-6994-7.

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.