Graduate Students Seminar

4pm Wedesday 10 March 2004

Brett Witty
MSI

Algorithmically classifying conjugacy classes of GL(n,q)

The seminar will be a gentle introduction to the use of conjugacy classes of the general linear group for enumeration problems in algebra. Only minimal knowledge of linear algebra is required.

For many enumeration problems in algebra we can interpret the problem as counting orbits of vectors under the action of some linear group. By the Cauchy-Frobenius Lemma this reduces to counting fixed points under this action and we can simplify this further by considering representatives of conjugacy classes of elements in the linear group. I will discuss a classification of the conjugacy classes and effective methods for algorithmically producing this classification.




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