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Zapiski Nauchnykh Seminarov POMI, 2022, Volume 511, Pages 54–99 (Mi znsl7209)  

This article is cited in 1 scientific paper (total in 1 paper)

Combinatoric of the karyon tilings

V. G. Zhuravlev

Vladimir State University
Full-text PDF (409 kB) Citations (1)
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Abstract: In this article, we study the combinatorial properties of the karyon tilings $\mathcal{T}$ of the torus $\mathbb{T}^d$ of an arbitrary dimension $d$. Our main results are the following statements: 1) the karyon corona $\mathbf{Cr}$ contains all types of polyhedral stars of the $\mathcal{T}$ tilings; 2) the number of all faces of dimension $a$ of the tiling $\mathcal{T}$ is equal to $md!/((d-a)!a!)$, where $m$ is the order of tilling.
Key words and phrases: toric karyon tilings, classification, symmetries, combinatorics, local rules.
Received: 06.01.2021
Document Type: Article
UDC: 511.3
Language: Russian
Citation: V. G. Zhuravlev, “Combinatoric of the karyon tilings”, Algebra and number theory. Part 5, Zap. Nauchn. Sem. POMI, 511, POMI, St. Petersburg, 2022, 54–99
Citation in format AMSBIB
\Bibitem{Zhu22}
\by V.~G.~Zhuravlev
\paper Combinatoric of the karyon tilings
\inbook Algebra and number theory. Part~5
\serial Zap. Nauchn. Sem. POMI
\yr 2022
\vol 511
\pages 54--99
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl7209}
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  • https://www.mathnet.ru/eng/znsl7209
  • https://www.mathnet.ru/eng/znsl/v511/p54
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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