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arXiv · 1701.06040

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

Andrea Ferraguti·Giacomo Micheli·Reto Schnyder
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Abstract

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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Andrea Ferraguti, Giacomo Micheli, Reto Schnyder. 2017-01-21. Irreducible compositions of degree two polynomials over finite fields have regular structure. https://doi.org/10.1093/qmath/hay015

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