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}
}```
• Published 2017
• Computer Science, Mathematics
• ArXiv
• 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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