# Finite Affine Groups: Cycle Indices, Hall-Littlewood Polynomials, and Probabilistic Algorithms

@inproceedings{Fulman2000FiniteAG, title={Finite Affine Groups: Cycle Indices, Hall-Littlewood Polynomials, and Probabilistic Algorithms}, author={Jason Fulman}, year={2000} }

- Published 2000
DOI:10.1006/jabr.2001.9104

The asymptotic study of the conjugacy classes of a random element of the finite affine group leads one to define a probability measure on the set of all partitions of all positive integers. Four different probabilistic understandings of this measure are given--three using symmetric function theory and one using Markov chains. This leads to non-trivial enumerative results. Cycle index generating functions are derived and are used to compute the large dimension limiting probabilities that an… CONTINUE READING

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## Proportions of Cyclic Matrices in Maximal Reducible Matrix Groups and Algebras

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