论文标题
带有相同长度的循环的rédei排列
Rédei permutations with cycles of the same length
论文作者
论文摘要
令$ \ mathbb {f} _q $为奇数特征的有限字段。我们研究了rédei函数，该功能诱导$ \ mathbb {p}^1（\ mathbb {f} _q）$，其周期分解仅包含长度$ 1 $和$ j $的周期，用于Integer $ j \ geq 2 $。当$ j $是$ 4 $或质量数字时，我们给出了这种类型的rédei置换的必要条件，以$ \ mathbb {p}^1（\ mathbb {f} _q）$存在，表征rédei置换量，由$ 1 $ - 和$ j $ cyccles组成，并确定其总编号。我们还根据固定点的数量和构建规定数量的固定点数量的Rédei排列的程序和程序提供了Rédei参与的明确公式，$ J $ -CYCLE的$ J \ in \ in \ in \ in \ in \ {3,4,5 \} $。
Let $\mathbb{F}_q$ be a finite field of odd characteristic. We study Rédei functions that induce permutations over $\mathbb{P}^1(\mathbb{F}_q)$ whose cycle decomposition contains only cycles of length $1$ and $j$, for an integer $j\geq 2$. When $j$ is $4$ or a prime number, we give necessary and sufficient conditions for a Rédei permutation of this type to exist over $\mathbb{P}^1(\mathbb{F}_q)$, characterize Rédei permutations consisting of $1$- and $j$-cycles, and determine their total number. We also present explicit formulas for Rédei involutions based on the number of fixed points, and procedures to construct Rédei permutations with a prescribed number of fixed points and $j$-cycles for $j \in \{3,4,5\}$.
