关于多元置换多项式的若干问题

There are a lot of known results on permutation polynomials in one variable, but the known results on permutation.polynomials in several variables are much less. Usually, problems on permutation polynomials in several variables have some new differiculty, which disappears in the case of one variable. It is shown by some old results. From algebraic geometric point of view, a permutation polynomial in several variables corresponds to a.morphism of relative codimension larger than 0. This project is devoted to the research to two class of problems on permutation polynomials in several variables (over finite fields or residue.rings).

本项目研究多元置换多项式的几个基本问题。主要目标是解决Niederreiter公开问题的二元情形并部分推广到多元情形；得到模p^n的置换多项式对n的递归判别法，推广Nobauer关于Ｓ嗬嗷飞弦辉没欢嘞钍降幕径ɡ怼Ｖ没欢嘞钍接攵喔鍪Х种в辛担鞘Чぞ叩氖匝榈兀⑶以诿苈搿⒈嗦氲攘煊蛴性嚼丛蕉嗟挠τ谩enstra的工作以后，多元多项式将倍受重视。