ENUMERATING LOCAL PERMUTATION POLYNOMIALS OVER RESIDUE CLASS RINGS

Abstract

Diestelkamp, Hartke and Kenney recently studied local permutation polynomials over finite field $F_s$ and proved that $2s-4$ is the sharp bound of their degrees when $s \gt 3$. In this paper, we focus on local permutation polynomials over residue class rings. We prove two specific formulas computing the number and the sharp bound of degrees of local permutation polynomials modulo $p^n$ respectively.