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Zapiski Nauchnykh Seminarov POMI, 2021, Volume 502, Pages 74–121 (Mi znsl7094)  

This article is cited in 2 scientific papers (total in 2 papers)

Symmetries structure of karyon tilings

V. G. Zhuravlev

Vladimir State University
Full-text PDF (402 kB) Citations (2)
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Abstract: In this article, we study the symmetry properties of the karyon tilings $\mathcal{T}$ of the torus $\mathbb{T}^d$ of arbitrary dimension $d$. Its main results are the following statements: 1) The tilings $\mathcal{T}$ are translation invariant relative to the canonical shift $S$ of the torus $\mathbb{T}^d$. This is a fundamental property of the karyon tilings. 2) Nondegenerate karyon tilings $\mathcal{T}$ have $2^d$ central symmetries.
Key words and phrases: toric karyon tilings, classification, symmetries, combinatorics, local rules.
Received: 31.03.2021
Document Type: Article
UDC: 511.9, 511.48
Language: Russian
Citation: V. G. Zhuravlev, “Symmetries structure of karyon tilings”, Algebra and number theory. Part 4, Zap. Nauchn. Sem. POMI, 502, POMI, St. Petersburg, 2021, 74–121
Citation in format AMSBIB
\Bibitem{Zhu21}
\by V.~G.~Zhuravlev
\paper Symmetries structure of karyon tilings
\inbook Algebra and number theory. Part~4
\serial Zap. Nauchn. Sem. POMI
\yr 2021
\vol 502
\pages 74--121
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl7094}
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  • https://www.mathnet.ru/eng/znsl7094
  • https://www.mathnet.ru/eng/znsl/v502/p74
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Записки научных семинаров ПОМИ
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    References:14
     
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