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Rational Functions Of Degree Five That Permute The Projective Line Over A Finite Field, Christopher Sze
Rational Functions Of Degree Five That Permute The Projective Line Over A Finite Field, Christopher Sze
USF Tampa Graduate Theses and Dissertations
Rational functions over a finite field Fq induce mappings from the projective line P1(Fq) to itself. Rational functions that permute the projective line are called permutation rational functions (PRs). The notion of permutation rational functions is a natural extension of the permutation polynomials which have been studied for over a century. Recently, PRs of degrees up to four have been determined. This dissertation is a project aimed at determining PRs of degree five.
Rational functions of degree five (excluding those that are equivalent to polynomials) are divided into five cases according to the factorization of their denominators. Our main results …