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}
}
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