Together with Marco Timpanella (University of Perugia) and Giovanni Zini (University of Modena and Reggio Emilia), the research group organize monthly seminars.
20 October 2026 [4.00 pm - Italian time] - Steve Wang (School of Mathematics and Statistics, Carleton University, )
Title: Permutation polynomials, projective polynomials, and bijections between µ_{(q^n−1)(q-1)} and PG(n-1,q)
Abstract: Motivated by the study of permutation polynomials over F_{q^2} and rational permutation functions over projective line, we introduce a class of bijections between the projective geometry PG(n − 1, q) and the set of roots of unity µ_{(q^n−1)/(q-1)} in finite field F_{q^n} for an arbitrary integer n ≥ 2 and any basis of F_{q^n} over F_q. This generalizes the well-studied Mobius transformations for n = 2 and a recent result by Qu and Li for n = 3. We also study a class of projective polynomials, using the coefficients and properties of which we determine the inverses of these bijections. Moreover, we study the roots of these projective polynomials and explicitly describe the correspondence between a partition of µ_{(q^n−1)/(q-1)} and a natural partition of PG(n−1, q). As an application, we can obtain several classes of permutation polynomials of F_{q^n} of index (q^n-1)/(q-1).