剩余类环上的置换多项式
Permutation polynomials over residue class rings
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摘要: 研究了一类典型的多元奇异多项式,得到了其为置换多项式的充要条件,推广了张起帆的结果.此外,得到了多项式为模3ω的置换多项式的充要条件,从而发展了Revest的结果.Abstract: A class of typical singular polynomials in several indeterminates is studied,and a necessary and sufficient condition for such polynomials to be permutation polynomials is obtained,which generalizes Zhang's result on the subject.Moreover,a necessary and sufficient condition for a polynomial in one indeterminate to be a permutation polynomial modulo 3ω is proved,which develops Revest's result.