J Austral Math Soc Ser A 43 pp171--175, 1987.

Permutation Polynomials in Several Variables over Residue Class Rings

H. K. Kaiser and W. Nöbauer

Abstract

The concept of a permutation polynomial function over a commutative ring with 1 can be generalized to multiplace functions in two different ways, yielding the notion of a k-ary permutation polynomial function (k > 1, k Î N) and the notion of a strict k-ary permutation polynomial function respectively. It is shown that in the case of a residue class ring Z_m of the integers these two notions coincide if and only if m is squarefree.

1980 AMS Subject Classification: 13B25

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Authors

H. K. Kaiser

W. Nöbauer

Institut für Algebra und Diskrete Mathematik, Technische Universität Wien, Wiedner Hauptstraße 8-10, A-1040 Vienna, Austria.