Abstract

Recently, rational functions of degree three that permute the projective line ${\mathbb{P}}^1({\mathbb{F}}_q)$ over a finite field ${\mathbb{F}}_q$ were determined by Ferraguti and Micheli. In the present paper, using a different method, we determine all rational functions of degree four that permute ${\mathbb{P}}^1({\mathbb{F}}_q).$

中文翻译：

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在有限域上置换投影线的四次有理函数

摘要

最近，置换射影线的三阶有理函数 ${\mathbb{磷}}^1({\mathbb{F}}_q)$ 在有限域上 ${\mathbb{F}}_q$由 Ferraguti 和 Micheli 决定。在本文中，使用不同的方法，我们确定所有四次置换的有理函数${\mathbb{磷}}^1({\mathbb{F}}_q).$