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| | {{Expert-subject|mathematics|date=November 2008}} |
| | 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 ''k''th component for ''k'' = 1, …, ''n'' is given by: |
| | :<math>P_k = \frac{k}{|G|} \sum_{g \in G} c_k(g)</math> where ''c''<sub>''k''</sub>(''g'') is the number of ''k''-cycles in the cycle decomposition of ''g''. |
| | |
| | ==Applications== |
| | The Parker vector can assist in the recognition of [[Galois group]]s. |
| | |
| | ==References== |
| | *{{cite book | title = Permutation Groups | author = Peter J. Cameron | publisher = Cambridge University Press | year = 1999 | isbn = 0-521-65378-9 | url = http://books.google.com/books?id=4bNj8K1omGAC&pg=PA48&dq=%22Parker+Vector%22&lr=&as_brr=0&ei=JeKoR8iKHIvsiQHfjNWqCg&sig=v2x98oF0YEsxyNm8HXq0BHPDXPA }} |
| | *{{cite book | title = Finite Geometries: Proceedings of the Fourth Isle of Thorns Conference | author = Aart Blokhuis | publisher = Springer | year = 2001 | isbn = 0-7923-6994-7 | url = http://books.google.com/books?id=P8Ra5zHVzQUC&pg=PA59&dq=%22Parker+Vector%22&lr=&as_brr=0&ei=JeKoR8iKHIvsiQHfjNWqCg&sig=yjCRM55fuSmS84OZ-ugc9tT2kyo }} |
| | |
| | {{DEFAULTSORT:Parker Vector}} |
| | [[Category:Permutation groups]] |
| | |
| | |
| | {{algebra-stub}} |
Template:Expert-subject
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:
- 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.
References
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- 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
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Template:Algebra-stub