Profinite approach to S-adic shift spaces II: Invertible directive sequences
Abstract
This paper is the second in a series about (relatively) free profinite semigroups and S-adic representations of minimal shifts. The first installment introduced the key notions of profinite images and saturating properties. The present paper examines the relationship between relative invertibility conditions (on a directive sequence) and charging properties (of a shift). The main result shows that the two properties are equivalent under mild conditions. Moreover, charging properties are shown to be equivalent to density of subgroups generated by return words in relatively free profinite groups. The main result can then be used to deduce purely discrete statements about subgroups generated by return words in relatively free groups. We also highlight applications of the main result to the study of maximal bifix decoding, following earlier work by the second author. Finally, we establish some results on the effect of direct images on charging properties and explain how to apply these results to the case of episturmian shifts.
Related
- Weighted boundedness of maximal operator associated with invertible linear transformations on variable Lebesgue spaces
- Universal Shift Congruences for Weighted Permutation Sequences
- On the weak invariance principle for strictly stationary sequences in some Besov spaces
- Pimp my fixpoint: sofic realization of multidimensional substitution-based shift spaces
- Reflexivity of Grothendieck Spaces and Strongly Normal Sequences
BibTeX
@misc{almeida2026profinite,
title = {{Profinite approach to S-adic shift spaces II: Invertible directive sequences}},
author = {Jorge Almeida and Alfredo Costa and Herman Goulet-Ouellet},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04737},
eprint = {2611.04737},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04737},
}
RIS
TY - UNPB
TI - Profinite approach to S-adic shift spaces II: Invertible directive sequences
AU - Jorge Almeida
AU - Alfredo Costa
AU - Herman Goulet-Ouellet
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04737
UR - https://arxiv.org/abs/2611.04737
AB - This paper is the second in a series about (relatively) free profinite semigroups and S-adic representations of minimal shifts. The first installment introduced the key notions of profinite images and saturating properties. The present paper examines the relationship between relative invertibility conditions (on a directive sequence) and charging properties (of a shift). The main result shows that the two properties are equivalent under mild conditions. Moreover, charging properties are shown to be equivalent to density of subgroups generated by return words in relatively free profinite groups. The main result can then be used to deduce purely discrete statements about subgroups generated by return words in relatively free groups. We also highlight applications of the main result to the study of maximal bifix decoding, following earlier work by the second author. Finally, we establish some results on the effect of direct images on charging properties and explain how to apply these results to the case of episturmian shifts.
ER -