# Irreducible compositions of degree two polynomials over finite fields have regular structure

@article{Ferraguti2017IrreducibleCO, title={Irreducible compositions of degree two polynomials over finite fields have regular structure}, author={Andrea Ferraguti and G. Micheli and R. Schnyder}, journal={ArXiv}, year={2017}, volume={abs/1701.06040} }

Let $q$ be an odd prime power and $D$ be the set of monic irreducible polynomials in $\mathbb F_q[x]$ which can be written as a composition of monic degree two polynomials. In this paper we prove that $D$ has a natural regular structure by showing that there exists a finite automaton having $D$ as accepted language. Our method is constructive.

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