论文标题
关于可逆序列的Skolem问题
On the Skolem Problem for Reversible Sequences
论文作者
论文摘要
给定整数线性复发序列$ \ langle x_n \ rangle_n $，Skolem问题要求确定是否存在自然数量$ n $，以便$ x_n = 0 $。 Lipton，Luca，Nieuwveld，Ouaknine，Purser和Worrell的最新工作证明了Skolem问题对于最多七个可逆秩序序列是可以决定的。在这里，我们提供了他们的结果的另一种证明。我们的小说方法对Galois共轭物采用了有力的结果，该偶联物位于两个同心圆上，这是由于迪比卡斯和史密斯而引起的。
Given an integer linear recurrence sequence $\langle X_n \rangle_n$, the Skolem Problem asks to determine whether there is a natural number $n$ such that $X_n = 0$. Recent work by Lipton, Luca, Nieuwveld, Ouaknine, Purser, and Worrell proved that the Skolem Problem is decidable for a class of reversible sequences of order at most seven. Here we give an alternative proof of their result. Our novel approach employs a powerful result for Galois conjugates that lie on two concentric circles due to Dubickas and Smyth.
