The dynamics of permutations on irreducible polynomials

2018/09/20 by Reis, Lucas, Wang, Qiang
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1809.07645

Abstract

We study degree preserving maps over the set of irreducible polynomials over a finite field. In particular, we show that every permutation of the set of irreducible polynomials of degree k over \mathbbF_q is induced by an action from a permutation polynomial of \mathbbF_q^k with coefficients in \mathbbF_q. The dynamics of these permutations of irreducible polynomials of degree k over \mathbbF_q, such as fixed points and cycle lengths, are studied. As an application, we also generate irreducible polynomials of the same degree by an iterative method.

Related

• Permutation polynomials from a linearized decomposition
• Dynamical Irreducibility of Certain Families of Polynomials over Finite Fields
• Generating series for irreducible polynomials over finite fields
• Permutation polynomials over finite fields by the local criterion
• Construction of irreducible polynomials through rational transformations