On a finite state representation of \(GL(n,\mathbb{Z})\)
It is examined finite state automorphisms of regular rooted trees constructed in [6] to represent groups \(GL(n,\mathbb{Z})\). The number of states of automorphisms that correspond to elementary matrices is computed. Using the representation of \(GL(2,\mathbb{Z})\) over an alphabet of size \(4\) a...
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| Date: | 2023 |
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| Format: | Article |
| Language: | English |
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Lugansk National Taras Shevchenko University
2023
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2158 |
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| Journal Title: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-21582023-12-11T16:21:07Z On a finite state representation of \(GL(n,\mathbb{Z})\) Oliynyk, A. Prokhorchuk, V. automorphism of rooted tree, finite state automorphism, integer matrix, free group 20E08, 20E22, 20E26 It is examined finite state automorphisms of regular rooted trees constructed in [6] to represent groups \(GL(n,\mathbb{Z})\). The number of states of automorphisms that correspond to elementary matrices is computed. Using the representation of \(GL(2,\mathbb{Z})\) over an alphabet of size \(4\) a finite state representation of the free group of rank \(2\) over binary alphabet is constructed. Lugansk National Taras Shevchenko University 2023-12-11 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2158 10.12958/adm2158 Algebra and Discrete Mathematics; Vol 36, No 1 (2023) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2158/pdf_1 Copyright (c) 2023 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
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| datestamp_date |
2023-12-11T16:21:07Z |
| collection |
OJS |
| language |
English |
| topic |
automorphism of rooted tree finite state automorphism integer matrix free group 20E08 20E22 20E26 |
| spellingShingle |
automorphism of rooted tree finite state automorphism integer matrix free group 20E08 20E22 20E26 Oliynyk, A. Prokhorchuk, V. On a finite state representation of \(GL(n,\mathbb{Z})\) |
| topic_facet |
automorphism of rooted tree finite state automorphism integer matrix free group 20E08 20E22 20E26 |
| format |
Article |
| author |
Oliynyk, A. Prokhorchuk, V. |
| author_facet |
Oliynyk, A. Prokhorchuk, V. |
| author_sort |
Oliynyk, A. |
| title |
On a finite state representation of \(GL(n,\mathbb{Z})\) |
| title_short |
On a finite state representation of \(GL(n,\mathbb{Z})\) |
| title_full |
On a finite state representation of \(GL(n,\mathbb{Z})\) |
| title_fullStr |
On a finite state representation of \(GL(n,\mathbb{Z})\) |
| title_full_unstemmed |
On a finite state representation of \(GL(n,\mathbb{Z})\) |
| title_sort |
on a finite state representation of \(gl(n,\mathbb{z})\) |
| description |
It is examined finite state automorphisms of regular rooted trees constructed in [6] to represent groups \(GL(n,\mathbb{Z})\). The number of states of automorphisms that correspond to elementary matrices is computed. Using the representation of \(GL(2,\mathbb{Z})\) over an alphabet of size \(4\) a finite state representation of the free group of rank \(2\) over binary alphabet is constructed. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2023 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2158 |
| work_keys_str_mv |
AT oliynyka onafinitestaterepresentationofglnmathbbz AT prokhorchukv onafinitestaterepresentationofglnmathbbz |
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2025-07-17T10:31:08Z |
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2025-07-17T10:31:08Z |
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1837890134101458944 |