论文标题
移动空间和希格曼 - 汤普森组的自动形态：单方面的情况
Automorphisms of shift spaces and the Higman--Thompson groups: the one-sided case
论文作者
论文摘要
令$ 1 \ le r <n $为整数。我们给出证明，$ \ mathop {\ mathrm {aut}}（{x_ {x_ {n}^{\ Mathbb {n}}，σ_{n}} $ n $ n $ n $ n $ n $ subgoloup $ $ \ math}的自动偏移的自动偏移的自动形态移动}自动晶体组$ \ mathop {\ mathrm {out}}}（{g_ {n，r}}）$的higman-Thompson组$ g_ {n，r} $。 From this, we can represent the elements of $\mathop{\mathrm{Aut}}({X_{n}^{\mathbb{N}}, σ_{n}})$ by finite state non-initial transducers admitting a very strong synchronizing condition. 令$ h \ in \ Mathcal {h} _ {n} $，并为代表$ h $的最小传感器的状态数写成$ | h | $。我们表明，$ h $最多可以写成$ | h | $扭转元素的产物。该结果增强了Boyle，Franks和厨房的类似结果，其中分解涉及更复杂的扭转元素，并且不支持实用的\ textit {a先验{先验估计结果的长度。 我们还探索了de bruijn图的折叠数量，并为这些折叠的折叠量为单词长度$ 2 $和字母尺寸$ n $提供了计数结果。 最后，我们提供有关$ \ Mathop {\ Mathrm {aut}}}}（{x_ {n}^{\ Mathbb {n}}，σ__{n}}）$的一些已知结果的新证明。
Let $1 \le r < n$ be integers. We give a proof that the group $\mathop{\mathrm{Aut}}({X_{n}^{\mathbb{N}}, σ_{n}})$ of automorphisms of the one-sided shift on $n$ letters embeds naturally as a subgroup $\mathcal{H}_{n}$ of the outer automorphism group $\mathop{\mathrm{Out}}({G_{n,r}})$ of the Higman-Thompson group $G_{n,r}$. From this, we can represent the elements of $\mathop{\mathrm{Aut}}({X_{n}^{\mathbb{N}}, σ_{n}})$ by finite state non-initial transducers admitting a very strong synchronizing condition. Let $H \in \mathcal{H}_{n}$ and write $|H|$ for the number of states of the minimal transducer representing $H$. We show that $H$ can be written as a product of at most $|H|$ torsion elements. This result strengthens a similar result of Boyle, Franks and Kitchens, where the decomposition involves more complex torsion elements and also does not support practical \textit{a priori} estimates of the length of the resulting product. We also explore the number of foldings of de Bruijn graphs and give a counting result for these for word length $2$ and alphabet size $n$. Finally, we offer new proofs of some known results about $\mathop{\mathrm{Aut}}({X_{n}^{\mathbb{N}}, σ_{n}})$.
