On the number of distinct functional graphs of affine-linear transformations over finite fields

@article{Bach2012OnTN,
  title={On the number of distinct functional graphs of affine-linear transformations over finite fields},
  author={E. Bach and Andrew Bridy},
  journal={Linear Algebra and its Applications},
  year={2012},
  volume={439},
  pages={1312-1320}
}
Abstract We study the number of non-isomorphic functional graphs of affine-linear transformations from ( F q ) n to itself, and we prove upper and lower bounds on this quantity as n→∞. As a corollary to our result, we prove bounds on the number of conjugacy classes in the symmetric group S q n that intersect AGLn(q). 
Counting distinct functional graphs from linear finite dynamical systems
Functional graphs of polynomials over finite fields
Dynamics of Endomorphism of Finite Abelian Groups
Counting dynamical systems over finite fields

References

SHOWING 1-10 OF 28 REFERENCES
Multiplicative complexity of polynomial multiplication over finite fields
  • M. Kaminski, N. Bshouty
  • Mathematics, Computer Science
  • 28th Annual Symposium on Foundations of Computer Science (sfcs 1987)
  • 1987
On Random Generation of the Symmetic Group
Transition graphs of affine transformation on vector spaces over finite fields
Partitions with "d(a) copies of a"
...
1
2
3
...