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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| Дата: | 2023 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2023
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2158 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| _version_ | 1856543143042744320 |
|---|---|
| author | Oliynyk, A. Prokhorchuk, V. |
| author_facet | Oliynyk, A. Prokhorchuk, V. |
| author_sort | Oliynyk, A. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2023-12-11T16:21:07Z |
| 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. |
| first_indexed | 2026-02-08T07:58:32Z |
| format | Article |
| id | admjournalluguniveduua-article-2158 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T07:58:32Z |
| publishDate | 2023 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-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 |
| 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 \(GL(n,\mathbb{Z})\) |
| title | 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_short | On a finite state representation of \(GL(n,\mathbb{Z})\) |
| title_sort | on a finite state representation of \(gl(n,\mathbb{z})\) |
| topic | automorphism of rooted tree finite state automorphism integer matrix free group 20E08 20E22 20E26 |
| topic_facet | automorphism of rooted tree finite state automorphism integer matrix free group 20E08 20E22 20E26 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2158 |
| work_keys_str_mv | AT oliynyka onafinitestaterepresentationofglnmathbbz AT prokhorchukv onafinitestaterepresentationofglnmathbbz |