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...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Datum:2018
1. Verfasser: Woryna, Adam
Format: Artikel
Sprache:English
Veröffentlicht: Lugansk National Taras Shevchenko University 2018
Schlagworte:
Online Zugang:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/822
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Назва журналу:Algebra and Discrete Mathematics

Institution

Algebra and Discrete Mathematics
id admjournalluguniveduua-article-822
record_format ojs
spelling 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
first_indexed 2025-12-02T15:37:12Z
last_indexed 2025-12-02T15:37:12Z
_version_ 1850411405950320640