The generalized dihedral groups \(Dih(\mathbb{Z}^n)\) as groups generated by time-varying automata
Let \(\mathbb{Z}^n\) be a cubical lattice in the Euclidean space \(\mathbb{R}^n\). The generalized dihedral group \(Dih(\mathbb{Z}^n)\) is a topologically discrete group of isometries of \(\mathbb{Z}^n\) generated by translations and reflections in all points from \(\mathbb{Z}^n\). We study this...
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Lugansk National Taras Shevchenko University
2018
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admjournalluguniveduua-article-8222018-03-22T09:42:02Z The generalized dihedral groups \(Dih(\mathbb{Z}^n)\) as groups generated by time-varying automata Woryna, Adam generalized dihedral groups, time-varying automaton, group generated by time-varying automaton 20E22, 20E08, 20F65 Let \(\mathbb{Z}^n\) be a cubical lattice in the Euclidean space \(\mathbb{R}^n\). The generalized dihedral group \(Dih(\mathbb{Z}^n)\) is a topologically discrete group of isometries of \(\mathbb{Z}^n\) generated by translations and reflections in all points from \(\mathbb{Z}^n\). We study this group as a group generated by a \((2n+2)\)-state time-varying automaton over the changing alphabet. The corresponding action on the set of words is described. Lugansk National Taras Shevchenko University 2018-03-22 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/822 Algebra and Discrete Mathematics; Vol 7, No 3 (2008) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/822/352 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2018-03-22T09:42:02Z |
| collection |
OJS |
| language |
English |
| topic |
generalized dihedral groups time-varying automaton group generated by time-varying automaton 20E22 20E08 20F65 |
| spellingShingle |
generalized dihedral groups time-varying automaton group generated by time-varying automaton 20E22 20E08 20F65 Woryna, Adam The generalized dihedral groups \(Dih(\mathbb{Z}^n)\) as groups generated by time-varying automata |
| topic_facet |
generalized dihedral groups time-varying automaton group generated by time-varying automaton 20E22 20E08 20F65 |
| format |
Article |
| author |
Woryna, Adam |
| author_facet |
Woryna, Adam |
| author_sort |
Woryna, Adam |
| title |
The generalized dihedral groups \(Dih(\mathbb{Z}^n)\) as groups generated by time-varying automata |
| title_short |
The generalized dihedral groups \(Dih(\mathbb{Z}^n)\) as groups generated by time-varying automata |
| title_full |
The generalized dihedral groups \(Dih(\mathbb{Z}^n)\) as groups generated by time-varying automata |
| title_fullStr |
The generalized dihedral groups \(Dih(\mathbb{Z}^n)\) as groups generated by time-varying automata |
| title_full_unstemmed |
The generalized dihedral groups \(Dih(\mathbb{Z}^n)\) as groups generated by time-varying automata |
| title_sort |
generalized dihedral groups \(dih(\mathbb{z}^n)\) as groups generated by time-varying automata |
| description |
Let \(\mathbb{Z}^n\) be a cubical lattice in the Euclidean space \(\mathbb{R}^n\). The generalized dihedral group \(Dih(\mathbb{Z}^n)\) is a topologically discrete group of isometries of \(\mathbb{Z}^n\) generated by translations and reflections in all points from \(\mathbb{Z}^n\). We study this group as a group generated by a \((2n+2)\)-state time-varying automaton over the changing alphabet. The corresponding action on the set of words is described. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/822 |
| work_keys_str_mv |
AT worynaadam thegeneralizeddihedralgroupsdihmathbbznasgroupsgeneratedbytimevaryingautomata AT worynaadam generalizeddihedralgroupsdihmathbbznasgroupsgeneratedbytimevaryingautomata |
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2025-12-02T15:37:12Z |
| last_indexed |
2025-12-02T15:37:12Z |
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1850411405950320640 |