论文标题
在collatz级集中的集群结构上
On the cluster structures in Collatz level sets
论文作者
论文摘要
可以在Collatz树的前几个级别集中观察到的簇结构，只要轨道稳定性\ [\ prod _ {\ prod _ {\ setack {k \ in r（n）\\ k \ equiv 4 \ equiv 4 \（\ equiv 4 \ equiv 4 \ equiv 4 \（\ arm {mathrm {mod}} \ 6）;从下面适当地界定树，其中$ r（n）$表示$ n $的collatz轨道。
The cluster structures that can be observed in the first few level sets of the Collatz tree are maintained through all its levels, provided that the orbit steadiness \[ \prod_{\substack{k \in R(n)\\ k \equiv 4\ (\mathrm{mod}\ 6)}} \frac{k-1}k \] of the elements $n$ of the Collatz tree is suitably bounded from below, where $R(n)$ denotes the Collatz orbit of $n$.
