We discuss a special class of permutation polynomials over finite fields focusing on some recent work on their factorization. In particular we obtain permutation polynomials with various factorization patterns that are favoured for applications. We also address a wide range of problems of current interest concerning irreducible factors of the terms of sequences and iterations of such permutation polynomials.

中文翻译：

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置换多项式和因式分解

我们讨论有限域上的一类特殊的置换多项式，重点是关于因式分解的最新工作。尤其是，我们获得了具有各种因式分解模式的置换多项式，这对应用程序是有利的。我们还解决了与此类置换多项式的序列项和迭代项的不可约因子有关的当前关注的广泛问题。