Communications of the
Korean Mathematical Society CKMS

In this paper, we give three criteria for non-polynomial functions interpolated from the set of univariate polynomials of degree less than $m$ over a finite field to be a permutation on the same set.

Keywords: $A_m$-permutation functions, $A_m$-permutation polynomials, extended Hermite-Dickson criterion, Carlitz polynomials, digit derivatives

MSC numbers: Primary 11T06; Secondary 11T55