论文标题
函数的迭代$ f：x^{k} \ rightarrow x $及其周期性
Iteration of Functions $f:X^{k}\rightarrow X$ and their Periodicity
论文作者
论文摘要
我们提出了一个迭代函数的概念$ f：x^{k} \ rightarrow x $，以表示形式$ a_ {n+k} = f（a_ {n}，a_ {n+1}，...，a_ __ {n+k-1}）$ a_ {n+k} = f（a_ {n}，a_ {n}）的重复关系。当它的$ n $ th iTerate是身份图时，我们将函数定义为$ n $ involutory，并讨论此类功能的基本群体理论属性以及它们与相应复发关系的周期的关系。此外，可以证明一个函数$ f：x^{k} \ rightArrow x $在其$ k $ grimuments中的每个$ k $ garmunty（持有其他固定）中都是$（k+1）$ - insutory。
We propose a notion of iterating functions $f:X^{k}\rightarrow X$ in a way that represents recurrence relations of the form $a_{n+k}=f(a_{n},a_{n+1},...,a_{n+k-1})$. We define a function as $n$-involutory when its $n$th iterate is the identity map, and discuss elementary group-theoretic properties of such functions along with their relation to cycles of their corresponding recurrence relations. Further, it is shown that a function $f:X^{k}\rightarrow X$ that is 2-involutory in each of its $k$ arguments (holding others fixed) is $(k+1)$-involutory.
