Any permutation polynomial is an n-cycle permutation. When n is a specific small positive integer, one can obtain efficient permutations, such as involutions, triple-cycle permutations and quadruple-cycle permutations. These permutations have important applications in cryptography and coding theory. Inspired by the AGW Criterion, we propose criteria for n-cycle permutations, which mainly are of the form $x^{r}h(x^s)$. We then propose unified constructing methods including recursive ways and a cyclotomic way for n-cycle permutations of such form. We demonstrate our approaches by constructing three classes of explicit triple-cycle permutations with high index and two classes of n-cycle permutations with low index, many of which are new both at levels of permutation property and cycle property.

任何置换多项式都是n周期置换。当n是一个特定的小正整数时，可以获得有效的置换，例如对合，三循环置换和四循环置换。这些置换在密码学和编码理论中具有重要的应用。受AGW标准的启发，我们提出了n周期置换的标准，其主要形式为$X^{\mathrm{[R}}H（X^s）$。然后，我们针对这种形式的n周期置换提出了统一的构建方法，包括递归方法和环原子方法。我们通过构造三类具有高索引的显式三循环置换和两类具有低索引的n循环置换来展示我们的方法，其中许多置换置换和循环性质都是新的。