A probabilistic heuristic for counting components of functional graphs of polynomials over finite fields

@article{Bellah2016APH,
  title={A probabilistic heuristic for counting components of functional graphs of polynomials over finite fields},
  author={Elisa Bellah and D. Garton and Erin Tannenbaum and N. Walton},
  journal={arXiv: Dynamical Systems},
  year={2016}
}
In 2014, Flynn and the second author bounded the average number of components of the functional graphs of polynomials of fixed degree over a finite field. When the fixed degree was large (relative to the size of the finite field), their lower bound matched Kruskal's asymptotic for random functional graphs. However, when the fixed degree was small, they were unable to match Krusal's bound, since they could not (Lagrange) interpolate cycles in functional graphs of length greater than the fixed… Expand
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