Let S be a set of monic degree 2 polynomials over a finite field and let C be the compositional semigroup generated by S. Inthispaper we establish a necessary and sufficient condition for C to be consisting entirely of irreducible polynomials. The condition we deduce depends on the finite data encoded in a certain graph uniquely determined by the generating set S. Using this machinery we are able both to show examples of semigroups of irreducible polynomials generated by two degree 2 polynomials and to give some non-existence results for some of these sets in infinitely many prime fields satisfying certain arithmetic conditions.
CITATION STYLE
Ferraguti, A., Micheli, G., & Schnyder, R. (2017). On sets of irreducible polynomials closed by composition. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10064 LNCS, pp. 77–83). Springer Verlag. https://doi.org/10.1007/978-3-319-55227-9_6
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