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  Finitely generated subgroups of free groups as formal languages and their cogrowth

Darbinyan, A., Grigorchuk, R., & Shaikh, A. (2021). Finitely generated subgroups of free groups as formal languages and their cogrowth. Journal of groups, complexity, cryptology, 13(2): Paper No. 1. doi:10.46298/jgcc.2021.13.2.7617.

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Datensatz-Permalink: https://hdl.handle.net/21.11116/0000-0009-FE5B-4 Versions-Permalink: https://hdl.handle.net/21.11116/0000-000C-3E7B-6
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Darbinyan-Grigorchuk-Shaikh_Finitely generated subgroups of free groups as formal languages and their cogrowth_2021.pdf (Verlagsversion), 512KB
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Darbinyan-Grigorchuk-Shaikh_Finitely generated subgroups of free groups as formal languages and their cogrowth_2021.pdf
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© A. Darbinyan, R. Grigorchuk and A. Shaikh This work is licensed under the Creative Commons Attribution License. To view a copy of this license, visit https://creativecommons.org/licenses/by/4.0/ or send a letter to Creative Commons, 171 Second St, Suite 300, San Francisco, CA 94105, USA, or Eisenacher Strasse 2, 10777 Berlin, Germany
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https://doi.org/10.46298/jgcc.2021.13.2.7617 (Verlagsversion)
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 Urheber:
Darbinyan, Arman, Autor
Grigorchuk, Rostislav1, Autor           
Shaikh, Asif, Autor
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Schlagwörter: Mathematics, Group Theory
 Zusammenfassung: For finitely generated subgroups $H$ of a free group $F_m$ of finite rank
$m$, we study the language $L_H$ of reduced words that represent $H$ which is a
regular language. Using the (extended) core of Schreier graph of $H$, we
construct the minimal deterministic finite automaton that recognizes $L_H$.
Then we characterize the f.g. subgroups $H$ for which $L_H$ is irreducible and
for such groups explicitly construct ergodic automaton that recognizes $L_H$.
This construction gives us an efficient way to compute the cogrowth series
$L_H(z)$ of $H$ and entropy of $L_H$. Several examples illustrate the method
and a comparison is made with the method of calculation of $L_H(z)$ based on
the use of Nielsen system of generators of $H$.

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Sprache(n): eng - English
 Datum: 2021
 Publikationsstatus: Online veröffentlicht
 Seiten: 30
 Ort, Verlag, Ausgabe: -
 Inhaltsverzeichnis: -
 Art der Begutachtung: Expertenbegutachtung
 Identifikatoren: arXiv: 2106.11552
DOI: 10.46298/jgcc.2021.13.2.7617
 Art des Abschluß: -

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Titel: Journal of groups, complexity, cryptology
Genre der Quelle: Zeitschrift
 Urheber:
Affiliations:
Ort, Verlag, Ausgabe: EDP Sciences
Seiten: - Band / Heft: 13 (2) Artikelnummer: Paper No. 1 Start- / Endseite: - Identifikator: -