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## Abstract

Let 1 ≤ r < n be integers. We give a proof that the group Aut(X

Let H ∈ ℋ

We also explore the number of foldings of de Bruijn graphs and give acounting result for these for word length 2 and alphabet size n.

Finally, we offer new proofs of some known results about Aut(X

^{ℕ}_{n},σ_{n}) of automorphisms of the one-sided shift on n letters embeds naturally as a subgroup ℋ_{n}of the outer automorphism group Out(G_{n,r}) of the Higman-Thompson group G_{n,r}. From this, we can represent the elements of Aut(X^{ℕ}_{n},σ_{n}) by finite state non-initial transducers admitting a very strong synchronizing condition.Let H ∈ 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*a priori*estimates of the length of the resulting product.We also explore the number of foldings of de Bruijn graphs and give acounting result for these for word length 2 and alphabet size n.

Finally, we offer new proofs of some known results about Aut(X

^{ℕ}_{n},σ_{n}).Original language | English |
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Article number | 15 |

Number of pages | 35 |

Journal | Discrete Analysis |

Volume | 2021 |

DOIs | |

Publication status | Published - 20 Sept 2021 |

## Keywords

- Higman--Thompson groups
- automorphisms of the shift
- Transducers

## Fingerprint

Dive into the research topics of 'Automorphisms of shift spaces and the Higman - Thompson groups: the one-sided case'. Together they form a unique fingerprint.## Projects

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