不存在定义Arshon序列和$σ$ -序列的迭代态射
There are no iterated morphisms that define the Arshon sequence and the $σ$-sequence
摘要：
Berstel证明了Arshon序列不能通过态射的迭代得到。这里给出了这一事实的另一种证明。$σ$ -序列是由Evdokimov为了在n维单位立方体中构造最大长度的链而构造的。事实证明，$σ$序列与龙曲线有密切的联系。证明了$σ$ -序列不能由态射的迭代定义。
英文摘要：
Berstel proved that the Arshon sequence cannot be obtained by iteration of a morphism. An alternative proof of this fact is given here. The $σ$-sequence was constructed by Evdokimov in order to construct chains of maximal length in the n-dimensional unit cube. It turns out that the $σ$-sequence has a close connection to the Dragon curve. We prove that the $σ$-sequence can not be defined by iteration of a morphism.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
