3 papers
math.CO2026
A new construction of permutation polynomials over
Zhiguo Ding, Xu Song, Wei Xiong
We determine all permutation polynomials among several families of polynomials over for arbitrary prime powers . We obtain some new families of permutation po…
math.NT2025
Determination of all complete mappings of F_{q^2} of the form aX^{3q}+bX^{2q+1}+cX^{q+2}+dX^3
Zhiguo Ding, Wei Xiong, Michael E. Zieve
For each prime power q, we determine all polynomials over F_{q^2} of the form f(X) := aX^{3q}+bX^{2q+1}+cX^{q+2}+dX^3 which induce complete mappings of F_{q^2}, in the sense that e…
math.NT2025
Exceptional extensions of local fields and the Carlitz--Wan conjecture
Zhiguo Ding, Wei Xiong, Qifan Zhang
For any prime power , a polynomial $f(X)\in\F_q[X]$ is ``exceptional'' if it induces bijections of $\F_{q^k}$ for infinitely many ; this condition is known to be equivalent t…