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Permutation rational functions over finite fields have attracted highinterest in recent years. However, only a few of them have been exhibited. Thisarticle studies a class of permutation rational functions constructed usingtrace maps on extensions of finite fields, especially for the cases ofquadratic and cubic extensions. Our achievements are obtained by investigatingabsolute irreducibility of some polynomials in two indeterminates.

On a Class of Permutation Rational Functions Involving Trace Maps