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Zapiski Nauchnykh Seminarov POMI, 2019, Volume 479, Pages 85–120 (Mi znsl6761)  
This article is cited in 7 scientific papers (total in 7 papers)

Local algorithm for constructing the derived tilings of two-dimensional torus

V. G. Zhuravlev

Vladimir State University
Full-text PDF (631 kB) Citations (7)
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Abstract: The local structure of the derived tilings $\mathcal{T}$ of two-dimensional torus $\mathbb{T}^2$ is investigated. Polygonal types of the stars in these tilings are classified. It is proved that in the nondegenerate case the tilings $\mathcal{T}$ contain 7 different types of stars and all types are representable by the stars with inner vertices from the crown $\mathbf{Cr}$ of the tiling $\mathcal{T}$. There sets the maximum principle being the basis of the $LLG$ algorithm for layer-by-layer growth of the derived tilings $\mathcal{T}$.
Key words and phrases: derived torus tilings, the classification of polygonal stars, local rules.
Received: 09.07.2019
Document Type: Article
UDC: 511.9, 511.48
Language: Russian
Citation: V. G. Zhuravlev, “Local algorithm for constructing the derived tilings of two-dimensional torus”, Algebra and number theory. Part 2, Zap. Nauchn. Sem. POMI, 479, POMI, St. Petersburg, 2019, 85–120
Citation in format AMSBIB
\Bibitem{Zhu19}
\by V.~G.~Zhuravlev
\paper Local algorithm for constructing the derived tilings of two-dimensional torus
\inbook Algebra and number theory. Part~2
\serial Zap. Nauchn. Sem. POMI
\yr 2019
\vol 479
\pages 85--120
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6761}
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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